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Strings 2008: Thursday



You may go to the main Strings 2008 page on this blog; that page includes the live webcast




Steve Gubser begins the Thursday session with a review talk about AdS/QCD and QCD at finite temperature: his PDF is here.

The first task is to find the free energy of the near-extremal D3-brane, whose metric is written down, at strong 't Hooft coupling. The result is 3/4 of the free result plus a term proportional to zeta(3). A few nuclear physicists joined the research of string theory - or at least they wrote down the Padé interpolation (ratio of polynomials) of the weak-coupling and strong-coupling formulae. (Planck was successful and exact in this business, so why not try again?)

Another slide is about the ratio of shear viscosity and entropy density - recall the 1/4.pi bound that remains the most popular quantity that has been reproduced by experiments. Viscosity is the divergence of "u" in the rest frame, he says, but it is instantly evaluated from a correlator of two copies of the stress-energy tensor. Meyer is very conservative - in Steve's opinion, too conservative.

The elliptic flow is an important phenomenon that can be measured experimentally: the pressure gradient is much larger in one direction than the transverse one (therefore the ellipse). He tries to parameterize it by ideal hydrodynamics but already a small viscosity changes a lot. Professionals can say what eta/s is favored and it agrees with the stringy value, even though some weak-coupling estimates would differ by an order of magnitude. Regimes tested by the RHIC (past) and LHC (future) is shown on a graph.

Steve returns to the theory and allows the bulk stringy AdS Lagrangian to be generalized, to include an arbitrary function. A choice gives very good agreement: not shocking that one function can reproduce another function. At least, he should get something interesting for the viscosity: some messy graphs are shown. If I understand well, this portion of the talk is only interesting for you if you know some recent hypotheses proposed by some heavy ion researchers, about a large viscosity at some transition. Steve thinks it can't work. Well, for me these are two rather messy and contrived pictures and I am agnostic about both, assuming that Steve knows more what he is doing.

The trailing string, another recent work of Steve and others, studies a quark that loses momentum: the loss rate is proportional to the momentum itself. The quark is an animal with a tail/string that probes the AdS bulk. This concept has links with the quark-antiquark static potential that he draws as the function of the distance. In this context, he compares string theory and lattice QCD.

Other graphs show what it means that "charm quarks flow", in the RHIC jargon. Some imperfect yet "respectable" agreement is blamed upon having N=4 instead of QCD: these are the fuzzy standards of QCD (and AdS/QCD). Frankly, I couldn't get too excited by a field where every answer to "does it work?" is so fuzzy.

Jet-splitting is beginning with data about quarks that can get out without interactions after some hard scattering: he shows what gets out as a function of an asimuthal angle. String theory says that the heavy quark is slowed down but he wants to know where the lost energy is going. He shows some flow chart, with a kind of vortex.

From heavy quarks, he gets to light quarks: jet quenching. Some broadening of momentum whose precise nature I didn't understand (transverse momentum squared goes like the distance, and the coefficient is to be calculated) is reproduced rather well by a Wilson line calculation, even though the perturbative answer is off by a factor of 3. Gubser decided to calculate the loss of a gluon's energy by a model with a falling chimney/string. The distance traveled is a 1/3-th power of some energy. He wants to include some response of gravitons etc. - I don't understand why exactly this thing.

At the LHC, one expects an even higher multiplicity from heavy ion collissions, tens of thousands, than at the RHIC. Gold collisions at RHIC make 38,000 particles or so - a number he wants to get from black holes in string theory, from the size of their horizon. So they get the entropy, from the trapped surface, 35,000. But that's clearly pure numerology. He even got some powers incorrectly (1/2 vs 1/3) and the numerical coefficient might be wrong, too. I don't quite know why he talks about this calculation at all.

To conclude, he thinks it's fun, close to experiment, and what makes it hard is that sometimes they're not comparing string theory directly to experiments but only to some prevailing and possibly wrong interpretations of the data. A very technical question: the answer is that reasonable people may sometimes disagree.

Cumrun Vafa asks why the equivalence should work in the first place. Answer: because of some universality in gauge theory. A repeated question from Cumrun is too deep - or vague? - for Gubser. ;-) I would say that Cumrun's complaint is identical to mine - he doesn't have a control over what should work and what shouldn't work. It's about a messy adaptation to random successes. Another question, from Juan Maldacena, is answered by stressing the importance of real-time evolution (over static things). Another question led to an explanation of the quasinormal modes that bring the black hole into the static shape after a time they were calculating.

Matthias Staudacher continues with a related topic, a review talk about the integrability of the AdS5 x S5 AdS/CFT with N=4 SYM on the boundary. The BPS, non-dynamical tests have worked for a long time. Recently, dynamical, non-BPS tests have worked beautifully, too, he claims.

Staudacher promotes these topics as philosophically pleasing, interdisciplinary, and linked to deep maths. A review of gauge theories - and N=4 - follows (the pretties theory). He says that it's not understood where its integrability comes from. There should be a field redefinition where it's manifest (it's clear neither from IIB nor from N=4 SYM). Superconformal groups of the background and IIB backgrounds are briefly explained.

Some words about spin chains. The energy is part of the (superconformal) symmetry here. The spectral problem of N=4 SYM is about the spectrum of operators in the theory and their dimensions. The classical problem (sigma-model) has been fully solved in terms of some curves. Also, the 1-loop dilatation operator has been diagonalized by a mapping it to an (integrable) Bethe Ansatz.

The BMN-like operators are mapped to a chain. At one loop, the interactions are near-neighbor. Long-range interactions arise at higher loops but the S-matrix is believed to factorize. The S-matrix found by people is unitary, obeys Yang-Baxter equation, and the crossing symmetry. He shows some messy all-loop Bethe equations. The system has surprising links to the Hubbard model. A function f(g) is shown to exactly agree in string theory and gauge theory. Staudacher invites people to calculate 3-loop things in string theory and 5-loop tests in gauge theory to improve some tests.

Pictures show hole distributions, not sure what the pictures exactly mean. They're of the type that they can only be understood if you've already seen all these answers. Add some SO(6) sigma-models - a full map between a limit of N=4 SYM and a thermodynamic Bethe Ansatz has been proven to work exactly 2 months ago. The Bethe Ansatz is not perfect: you can only trust it up to L loops where L is roughly the length of the operators (plus one), because of some wrapping problems. There are new ideas how to fix similar bugs.

Sometimes, more answers are known than the questions again. We don't even have the full 2-loop dilatation operator (in all sectors), so what are we diagonalizing, he asks? He wants to know other integrable CFTs, too. A commercial break: he announces regular annual conferences on integrability since 2005 (in 2008: Utrecht, in 2009: Potsdam). Outlook: young people can participate in exact solutions of N=4 SYM theory for the first time. A few questions. One question was about multitrace operators. Answer: that's many chains, not been solved so far.

After the coffee break, Shiraz Minwalla (see fisherman and pole) continues by deriving nonlinear fluid dynamics from gravity: PDF here. ;-) Shiraz begins with the same energetic vibrations that you know e.g. from Superheroes haha. He specifically promotes two students of him, Bhattacharyya and Loganayagam. Sorry, I can't remember the exact names so far but I will surely learn them later: so far, copy-and-paste from SlavaM's comment was enough, thanks! ;-)

Shiraz explains that N=4 should have the 't Hooft limit, known from Maldacena 1997 to be IIB on AdS5 x S5. In the AdS/CFT map, local things may get mapped to nonlocal mess. However, he will show that in a sector, the right boundary dynamics is local.

To get there, he considers a general AdS 2-derivative theory, truncates it to AdS Einstein gravity. He will mostly prove the following map: all long-wave solutions of Einstein's equations can be mapped to Navier-Stokes equations solutions, with the values of transport coefficients determined holographically.

Two solutions are first examples: empty AdS and a boosted (by velocity "u") version of AdS Schwarzschild at temperature "T". The boundary stress tensor equals to a power of temperature times a general u-dependent tensor. For an arbitrary (time-dependent) stress tensor on the boundary, he defines Delta(x) - minimum length scale of variations - and epsilon = 1/(T.Delta). The question is what constraints for the stress tensor he can derive generally from AdS/CFT and Einstein's equations in the bulk. Nice.

Naively, tubes should connect the boundary points with regions in the bulk, i.e. with constant x_mu in Schwarzschild coordinates. Wrong, problems with causality, metric not regular. The first improvement are tubes that go along incoming geodesics. Surprisingy easy to implement, 15 linear differential equations come out. 14 are independent: 4 are constraints (conservation of the stress tensor up to an order; independent of fluctuations of "g") and 10 are dynamical (M g_n = s_n) with a source. Regularity of the future horizon has to be assumed. Together with one more assumption, the solution is fully determined. So the solution only depends on the temperature and velocity (and the metric), but not arbitrary functions you would have a priori.

So there's map between Einstein's equations and generalized (higher-derivative-terms-including) Navier-Stokes solutions. This includes higher-order terms and confirms the eta/s=1/4.pi value. Shiraz also says the word "RHIC" because Juan told me to say the word. ;-)

Their solutions are singular at r=0 but under some assumptions, it's shielded by event horizons - the unique null manifolds that reduce to the black hole one in far future. The holographic translation of the growing horizon area in the bulk is probably something like an entropy-density-current on the boundary, unless I am deluded. Various comments (too fast) which stress tensors agree up to the second order etc. Shiraz is speeding up, approaching the speed of light and the Planck frequency. :-)

A possible extension of their work is to (non-universally) add non-metric (gauge...) fields in the bulk i.e. charge densities to the boundary. In conclusions, generalizations should exist; turbulence should be dually found in gravity (rotating black holes); time-reversal-symmetry breaking; reinterpreting cosmic censorship in the hydro variables; some N^2 scaling. Thank you - and everything abruptly slows down to 1/100 of his rate. ;-)

Hirosi asks about the fate of Navier-Stokes singularities. Shiraz answers that one can't trust the solutions below the inverse temperature distance scale, if I am simplifying it correctly. Another question about causality: these problems only occur if you truncate the solution up to a finite order. Another question: what happens with the epsilon expansion above one? The map breaks down because of the extra 5th dimension in the bulk. Answer rephrased in terms of quasinormal modes, too: infinitely many new modes generate nonlocalities that are equivalent to the integrating out of many KK modes. Enjoyable talk.

Luis Alday talks about the AdS/CFT calculation of the gluon (N=4) scattering amplitudes (with Maldacena): PDF here. You have n gluons, L loops, infrared divergences, etc. Make them finite in 4-2.epsilon dimensions. I like his accent - similar to the Italian who went to Malta. Compare e.g. "finite piece" and "piece on the table" or "worldsheet" with the "sheet on the bed". ;-) He draws the disk for the amplitude and makes a duality that maps the problem to a Wilson line, I suppose, in the dual AdS5 space (as in the dual conformal symmetry). This is probably the key moment and he didn't explain it too well.

To show in practice, he considers a 2-to-2 scattering. Assume s=t, Mandelstam variables coincide. They reduce the scattering problem to finding the minimum surface that ends at a sequence of light-like segments. And it probably works. Not so fast. He gets IR divergences which is OK, he says (on both sides). The result, in a hypergeometric form, must be expanded in epsilon.

In the last five minutes, he shows some newest results, about the translation of Ward identities into dual Ward identities. Up to 5 gluons, things are determined, so he goes to n=6 and n=infinity. Explicitly, BDS Ansatz fails for n=6 - I suppose we have already heard it. The MHV amplitudes are related to Wilson loops. Because the calculations didn't depend on S^5 and fermions, he believes there's some universality here. Another hard task involves mesons - not solved yet but the singular nature has been understood. If you find a minimal surface for 6 gluons, Alday invites you for dinner. He also wants to reproduce the Gross-Mende trick here and repair the BDS Ansatz. The integrability hasn't been used here yet.

Cumrun Vafa says that the surface carries more information than the area - can you recover the shape from the amplitudes? Answer (not too interesting one): he's only interested in the area.

Finally, Andrei Starinets wanted to offer another talk about the application of N=4 to heavy ion physics (he disapproves my label AdS/QCD for him and his collaborators, stressing that he is doing exact science, but I will keep on using AdS/QCD for everyone who wants to apply stringy holography to the observable nuclear physics!), focusing on finite densities and low temperatures, but he slightly changed the topic to the holographic description of quark-gluon plasma.

After some remotely related words about AdS/QCD, he asks about the difference between proton-proton and gold-gold scattering. He shows a graph of energy density vs. temperature - growing up to some point and then almost constant. The task now is to compute the transport coefficients from the dual gravity: all of them should be included in the quasinormal spectrum. All of them (viscosities, diffusion coefficients) for N=4 have been calculated up to the first order (and mostly to the second order). E.g. eta/s is drawn as a function of lambda, ending at 1/4.pi. A numerical bug was recently fixed. Later, he was showing nucl-th physicists fitting a curve. There are now 3 mostly independent proofs of the eta/s=1/4.pi value=0.08. Various other systems are known to have higher values; QCD seems to minimize among empirically known systems.

Finally, he wants holography to teach us about quantum Bose/Fermi liquids. The specific heat scales like different powers of "T" at low "T". They have different excitations etc. Fermi liquids explained by Landau who died on the year when string theory was born (and Czechoslovakia occupied, as your humble correspondent adds): he's not sure about the significance of this discovery, and neither am I. ;-)

He jumps to some D7-probe Karch-Katz stuff, trying to compute specific heat at low temperatures and the charge density (retarded) correlator (of j0,j0), especially the poles. He looks for propagating modes, a new type of sound. He suggests that the holographic dual is a non-Bose, non-Fermi, new kind of liquid. To conclude, many things have been found already but more will be helpful for non-equilibrium QCD and ALICE at the LHC will bring new high-temperature data.

A question is what he means by holographic dual for hypermultiplets that make it weakly coupled in the IR. Not sure about the answer. After the talk, someone says that he meant ATLAS, not ALICE. I actually think he did mean ALICE - the Pb ions. But Starinets surrendered and said it was ATLAS. ;-)

Later, Andrei explained me that, of course, he wants ALICE, but he used an incorrect picture of ATLAS, and someone just told him (correctly) that the picture was incorrect.

Herman Verlinde began the afternoon session with holographic gauge mediation (of SUSY breaking), an AdS_5-like dual description of a hidden sector where SUSY is broken: PDF here. After a few sentences, the computer (Mac) started to behave funnily. Fixed. String phenomenology may be studied from the top down, from the bottom up (decouple gravity; see Vafa's talk and others), and to study strongly coupled theories that may be uncovered by the LHC. Imagine that the LHC finds some new technicolor/composite physics, with a new hidden sector. This sector couples to gravity, visible gauge fields, and other fields.

Herman now learned the two arrow keys. ;-) If the hidden mass scale is well above a TeV, integrate the hidden sector out and see the new soft terms. If the new stuff is light, you have to include it. Now, he apparently wants to study the AdS bulk dual of the hidden sector only. The visible fields (IR) define the boundary conditions of the AdS-like space; references to holographic RG. General gauge mediation by Maede, Seiberg, Shih is outlined. Klebanov-Strassler (i.e. conifold; SU(N) x SU(M+N)...) is now assumed to be the hidden sector. The dynamical nature of the SUSY breaking is reflected by normalizability of a mode. At least 5 D7-branes needed for a SU(5) global symmetry.

The gaugino mass is localized in the IR region of the D7-brane, separated from the Standard Model (stringy kind of "gaugino mediation"). This mediation may be obtained as a limit of gauge mediation with many messenger fields (thus enhancing one particular term). Such a large number will bring Landau poles closer, and this is a real problem visible in the bulk picture, too. You can trust this game in a small window only.

In the last five minutes, he wants some SM particles to be composite - "mesons" of the higher-energy theory. These fields now go to the bulk. One needs intersecting D7-branes. Among conclusions that repeat the stuff above, Herman recommends to study a merger of his idea - holographic dual of strongly-coupled hidden sectors - and Vafa et al.'s F-theory phenomenology. A Hirosi Ooguri's question is answered by saying that something was only true qualitatively, some backreaction was neglected.

David Shih talks about general gauge mediation, a paper also mentioned by Herman above. It's work with Maede and Seiberg (and another collaborator, Buican, a new paper in progress). He clarifies the comment that the LHC is behind the corner: it is actually across the street. ;-)

David will talk about SUSY because he believes it's the best motivated scenario for the LHC. It must be broken; in a new hidden sector; it must be communicated to the MSSM. He will focus on his preferred mediation, gauge mediation. It's communicated via MSSM gauge bosons which are flavor-blind, and thus the flavor-changing neutral currents are absent. The spectrum is viable, calculable, and predictively distinctive.

He wants to divide the predictions of gauge-mediated models to general and model-dependent.

David begins with "ordinary" gauge mediation from the 1990s (Dine, Nelson, Nir, Shirman). Keep only the X superfield (spurion) = M + theta^2 F. M breaks R-symmetry, the other F breaks SUSY. Superpotential X.phi^2 couplings create splittings; phi is in real reps of the SM. He gets 1-loop diagrams for gaugino masses and 2-loop diagrams for sfermion masses.

A slide already divides the features to general and specific. Gaugino unification, sfermion hierarchy, and identity of NLSP can be shown non-universal by a simple beyond-ordinary gauge-mediated model.

The hidden sector must generally breaks SUSY; contain messengers; decouple from MSSM in the g=0 limit. To look at the limit, assume the group G only, not the detailed dynamics. So what you can study are correlators of global currents (as in QCD before it was known). The current "J" is a whole real superfield. In components, he writes various 2-point functions as a function of x^2 in x-space. Some of them vanish for unbroken SUSY. Because the breaking is spontaneous, these coefficients must have a nice x=0, either zero or constant in one case or another.

He weakly gauges the G=U(1) group and integrates the hidden sector out. The last step changes the U(1) beta-function and generates soft masses in the effective action. Now, when he adds SU(2) and SU(3) to U(1), too, gaugino unification evaporates. Absence of FCNCs survives while CP-problems may occur. Sfermion masses were positive in all old examples but counterexamples (tachyonic) were found later. The typical momentum in the integral is M so you can't get it from low-energy effective field theory.

Sfermion masses are independent of gaugino masses as well as gauge couplings. A couple of sum rules seem to be general. Five different sfermions f=Q,U,D,L,E per generation are functions of three parameters A1,A2,A3, so there must be 2 relations: Tr(Y m^2) = Tr((B-L)m^2) = 0. Corrected by RG flow to the weak scale. To summarize, they have identified variables to study gauge mediation in general. They have 3 complex (gaugino masses) plus 3 real (sfermions) parameters. Can you cover this 9-real-dimensional parameter space by a simple model? Carpenter et al. have the right number of parameters but not sure whether they cover everything. Other tasks is to apply Herman's methods; and to solve the mu/Bmu problem, general for gauge mediation. The LHC will judge us.

It will inspire fear, put many models to the test, and most models to the rest. A picture of Terminator with the governor of California. A question: why something is small? Answer: because we say it is small. ;-) Later, he said it can be seen from 2-point functions. Cumrun Vafa says that to solve the mu/Bmu problem, he has to require more than one g=0, and David agrees. Simeon is too far, the echo makes it harder to hear. David says that they have no new solutions of the problem but he doesn't know whether a problem can be solved.

Romuald Janik will begin the last pair of lectures with comments on 4-loop (!) perturbative Konishi from the AdS5 x S5 sigma-model. Right before he began, an organizer noticed on my blog that Vafa, Maldacena, and Polchinski share the 2008 Dirac Medal, so there was some applause. ;-)

Romuald's beginning is motivation. He will define the Konishi operator, explain why 4 loops matter etc. The task is nothing less than to find spectrum of N=4 SYM for any 't Hooft coupling in the planar (large N) limit. He wants to do it in the light-cone uniform description of AdS5 x S5. One needs a very strongly coupled regime, so some integrability tricks will be needed.

The Konishi operator is Tr(Phi_i^2) summed over the six values of "i". He really wants to take Tr(Z^2 X^2) from the same multiplet. The known dimension looks like Delta = 4 + 12g^2 - 48g^4 + 336g^6 plus a horrible multiple of g^8 whose coefficient includes an integer, an integer multiple of zeta(3), and another of zeta(5). The four-loop result is interesting because it's the first one where the Bethe Ansatz breaks down (wrapping interactions) - a sensitive test how we understand the theory.

First he, extremely quickly, reviews the 1-, 2-, 3-loop results from the Bethe Ansatz. The 4-loop result is wrong here; the wrapping graphs that are missing have mess all over around the cylinder with the BMN-like operator at the circles at the boundaries. The spin chain is not useful because it is exactly equivalent to the Bethe Ansatz.

There are two ways how the virtual particles can encircle the cylindrical graph. One needs some relativistic rules to be generalized to non-relativistic worldsheet theories (relevant for AdS) and the whole stuff must be applied to the Konishi operator. The correction goes like an exponential; the exponent in the truly relevant case involves arcsinh. At weak coupling, he can expand to see that the leading terms are at 4 loops.

He's going to solve it iteratively by excited state TBA e.g. sinh-Gordon or SLYM. The 0th order are Bethe equations while 1st order corrections shift both momentum as well as energy (by an F-term of a sort). The momentum shift actually enters only at 5-loop. Also some poles may be neglected. So he writes the formula for "Delta E" only, the F-term. It's written as an infinite sum (over Q) of an infinite integral (over some intermediate momentum q) of some product of "S S" with many additional indices; "S" is the S-matrix. The "Q" labels magnon-like particle species that can run in the loops, including bound states. There are two types: su(2) bound states (symmetric representation) and sl(2) (antisymmetric, physical in the mirror theory). The latter sl(2) states should be used here.

The scaling is "g^8", of course, and the rest is computed via residues. The zeta-functions here explicitly arise here from the summation over "Q", the tower of bound states. Everything else turns out to be integer. And a full agreement with a Zanon et al. perturbative calculation is obtained.

When he looks at it, he finds the 324+864zeta(3)-1440zeta(5) surprisingly simple, not too transcendental. ;-) For su(2), he would obtain much messier stuff. He obtained the corrections in a way that is alien for spin chains but normal for 2D QFT. The agreement is a spectacularly nontrivial confirmation of AdS/CFT. A question was answered by an analogy with some Zamoldchikov papers.

Finally, Carlo Rovelli will try to convince the auditorium to unlearn, forget, and abandon almost everything they know (and said) about physics and jump to loop quantum gravity. He's very honored to be there and assumes that everyone is honored to see Rovelli. ;-)

He assumes that no one knows anything about LQG, which is probably not correct. The abstract suggests that the talk will be identical to the basic notions described e.g. in his review 10 years ago: you can make a career out of 5 page of nonsense that you keep on repeating for decades. What are loops, what is kinematics, dynamics here, and what has been achieved (not sure what he will say in this section). ;-)

Rovelli advertises his book and says that LQG is studied by 200 people. On the first slide, he claims that no new physics is needed and perturbative divergences of gravity are just illusions. This is all such a breathtakingly stupid case of wishful thinking that I might lose my patience and turn off the video, in which case I would apologize that this text is truncated.

He claims that general relativity is "two different theories" which leads to "misunderstanding between communities". I am afraid it will continue to lead to misunderstanding, very politely speaking. He offers some bizarre statement that fields in spacetime are something else than fields in geometry of spacetime, or something like that. It makes no sense whatsoever.

Fine, why loops? So he reminds the people of Wheeler-DeWitt and similar stuff and promises that loops solve everything. OK, why loops? Now, he could just say that they're open Wilson lines connected by gauge-invariant vertices. People in the room know how to calculate 4-loop terms in things like Wilson lines. Instead, he wastes the time of the auditorium (and mine) by confused presentation of some undergraduate stuff. Instead of saying what he means in one sentence (every other speaker would need roughly 5 seconds for this stuff - someone only 1 second which is too fast), he goes through basic lectures of lattice gauge theory. He is either unaware of the word "Wilson loop" or thinks that people around don't know what a "Wilson loop" is. How dumb this guy must be? Let me omit these trivialities.

In his opinion, Wilson lines in a continuum are "too singular". Well, it depends. Then he claims that two previous problems cancel against one another because diffeomorphism invariance removes the "singular" nature of the space. It is easy to see that it does not (once you try to add *any* dynamics). He continues with some elementary stuff about "connections" and "Ashtekar variables". I am convinced that most people in that room have heard about these things already. Sorry, I have heard this very same stuff about 15 times already; they think that by constant repetition, they can imprint some nonsense to someone's or everyone's head. Except that this is not how it works in science.

Childish slides about "loops" and "strings" being both 1-dimensional follow, together with wrong statements that he can define the volume operator on his Hilbert space. It's known that you can't, it's singular (unlike the areas). He also says a lot of wrong statements about the finiteness of the Hamiltonian. See e.g. Nicolai et al. 2005, the most cited LQG paper in 2005, that explains that these things cannot be well-defined (without an infinite number of continuous ambiguities).

When he tries to talk about the path integral (spin foam in his case), he spends several sentences about Feynman's thesis, apparently assuming that the participants have probably never heard about the path integral. His talk is clearly not addressed to experts of any kind and he has clearly no idea what the physicists in the room are doing, not even approximately.

"Loop cosmology" is mentioned as an "application" of this pseudoscience. The usual misconceptions about the "removed singularities" are repeated. Nothing like that is removed, however. The infinite-dimensional dependence on the cutoff remains both in LQG and loop cosmology; it is only translated to the infinite-dimensional uncertainty of the Hamiltonian, just like in any other case of brute force cutoff regularization. Untrue statements about black hole entropy are added. These people are simply liars. They must know that what they're saying is just not true because there are hundreds of papers showing this fact with complete clarity and they must have seen at least some of them.

Simeon Hellerman asks what the can Rovelli possibly mean by a "black hole" if he doesn't even have the right low-energy limit (whose solution the black hole normally is defined to be). The second question is about the coefficient 1/4 and its universality (which is known not to be universal); Rovelli only admits that it is an issue. Concerning the first question, Rovelli talks about different definitions of horizons - which is completely irrelevant because he can't apply any definition of the horizon if he can't localize the Einstein-Hilbert limit with the smooth space in his Hilbert space.

Someone else says that Rovelli is in a topological phase - a polite way of saying that he incorrectly treats the groups. In the proper treatment, one gets the gravitons from reducing diff to the Lorentz group; gravitons transform under the latter. Rovelli tries to prove that a theory that satisfies all the group properties of a topological theory is not topological. ;-) Michael Douglas asks whether the LQG people have tried to make a contact with the important advances in 3D gravity by Strominger and others (much more solvable). Rovelli has, of course, no idea about the work going on in actual physics, in 3D, 4D, 10D, or any other dimension. He has only heard a remotely related 3D talk by Maloney. So somebody should sit down, he says.

Someone else asks why they could change the value of the Barbero-Immirzi parameter, from Penrose's gamma=i to ln(2)/sqrt(3).pi or something like that (see the quasinormal story on quasinormal modes). Rovelli says that "gamma" is analogous to theta_{QCD} and the value in the quantum theory should be carefully chosen. It's no contradiction, he says. Of course that it is a contradiction because they either obtain a wrong value of the black hole entropy or a wrong Newton's constant at low energies (assuming no divergences and flowing, as he likes to say). Another question is from a person who knows that LQ cosmology cannot be derived from LQG: it is not a reduction. Rovelli admits it cannot be derived, except for hand-waving (randomly modifying the theory). Thank God, it's over. Applause.
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reader Doug said...

Hi Lubos,

I do like one approach that seems new for Rovelli and may be somewhat comparable to an idea of Kapustin and Witten in Electric-Magnetic Duality And The Geometric Langlands Program, page 89, fig 4 “A schematic depiction of the four-manifold SIGMA×C“ and page 120, fig11 “Insertion of an ’t Hooft operator changes the topology of a G-bundle“. Note the PDF page counter is +1 relative to the actual page number.

This is the use of a cylinder in covariant dynamics: spinfoam beginning on Rovelli slide #29 but best seen on slide #30 [each on #15of 20 per PDF count].

The cylinder from my perspective may represent the globally curved, but locally flat virtual surface of an electron or planet revolving about a proton or star [the dot in both Rovelli and Witten diagrams], respectively.

The actual trajectory is a diagonal on a 2D surface [globally and locally flat] which becomes an helix on the cylindrical surface [twistor trajectory ?].

Since a cylinder is formed intermediate to a torus from a 2D surface and all may have solenoidal properties as in thermophysics:

a - I visualize Heisenberg matrix mechanics on a 2D surface with the diagonal as both and additive trace and sqrt(sum of squares of diagonal entries)=MIN(periodic travel distance).

b - I think this is equivalent to Schroedinger wave mechanics on a 3D surface with the diagonal becoming an helix but retaining equivalent trace and sqrt properties.

c - One correction that I would make to the Rovelli is that the interior shaded rectangle becomes helicoid in shape; since I also suspect that an entity travels simultaneously in both the SIGMA and C directions of Kapustin and Witten.

Note that Kapustin and Witten use the word loop in page 89, fig 4.


reader Luboš Motl said...

Dear Doug, what you write doesn't indicate that there is any relationship, not even a remote one, between the Witten-Kapustin concepts on one side and spin foam on the other side.

The word "loop" is used by (real) physicists all the time. Loops as in Feynman diagrams encode all the quantum corrections to a classical behavior; Wilson and 't Hooft loops are important "extended" observables in gauge theories.

The latter (Wilson loops) are indeed related to loops in loop quantum gravity except that these loops were not discovered in loop quantum gravity; and when one is using them correctly, they have nothing to do with gravity (in the same space where they're drawn, maybe in a higher-dimensional space related by holography).

Best
Lubos


reader Carlo Rovelli said...

Dear Lubos,
in the past I have never directly answered your comments about Loop Quantum Gravity and about myself, since I have a certain difficulty in relating to your communication style; but if you do not mind, I would like to have this response to your account of my STRINGS 08 talk posted in your website.

You write: "Carlo Rovelli will try to convince the auditorium to unlearn, forget, and abandon almost everything they know (and said) about physics and jump to loop quantum gravity."

This was not my objective. My objective was double. First, to tell the audience about an attempt to construct a background-independent quantum field theory. Second, to recall that string theory is not "everything we know about physics": it is a very interesting candidate for a fundamental theory. It is possible that the real world is described by string theory, but it is also possible that it is not. We should not mistake the beautiful achievements of string theory for acquired knowledge about the real world.

You write: "He's very honored to be there and assumes that everyone is honored to see Rovelli."

No, I did not assume so. I really felt honored by the invitation. I think that if you, or the readers of this blog were invited to talk at this conference, you or them would feel honored as I was. I did not think anyone at the conference felt honored to see me: I think that some people were curious, some indifferent, and a few were even a bit annoyed. Those few included probably yourself and David Gross, from what he said to me, but they formed a small minority. Those who invited me, the many people who listened to my talk with attention, the large number of people that asked questions to me, were genuinely interested, seems to me. I think this is very good. We do not know what is beyond the standard model and classical general relativity, and if a research community closes in itself with the arrogance of knowing The Ultimate Truth, it makes a mistake. Far from me believing that Loop Quantum Gravity is the Sure Answer; and I was very pleased to see again, from this invitation and from the way my talk was received, that many people in the String community are equally open.

You write: "He assumes that no one knows anything about LQG, which is probably not correct."

Here you right. I was uncertain on whether to focus on recent developments, talking to those who already know about LQG (like you, for instance), or give an introduction talk. I chose the second option because I was more interested in communicating to the large number of younger people at the conference, rather than to the senior scientists. I made this choice contrary to the advice of some colleagues; the reason is that I have great scientific respect for the leaders of string theory, but I do not think that they are the ultimate judges of the value of my work, like I am not the judge of theirs. Waiting for experiments capable of shedding real light, the judges are the young people, who will follow what they think is more interesting and promising. I wanted to talk to them.

You write: "The abstract suggests that the talk will be identical to the basic notions described e.g. in his review 10 years ago."

This is correct. A good part of the talk reported results that have today more than 10 years. Then there were the new results: the LOST theorem, loop cosmology, the resolution of the R=0 black hole singularity, the calculation of the n-point functions and the low energy limit, and many others ...

You write: "On the first slide, he claims that no new physics is needed..."

This is not what I said. I said that new physics beyond the standard model may very well be there, but this is not the problem I address. The problem I address is the possibility of defining a background independent QFT. LQG studies the hypothesis that this problem can be addressed in the context of quantum general relativity plus the standard model.

You write: " ... and perturbative divergences of gravity are just illusions."

This is not what I said either. I said that they might be produced by the fact that the usual expansion is around the wrong vacuum. This is an hypothesis taken seriously by many people, within and without LQG.

You write: " ... This is all such a breathtakingly stupid case of wishful thinking that I might lose my patience and turn off the video."

I think I am not commenting this. But I am glad you did not turn off the video.

You write: " ... He claims that general relativity is 'two different theories' which leads to 'misunderstanding between communities'. I am afraid it will continue to lead to misunderstanding, very politely speaking. He offers some bizarre statement that fields in spacetime are something else than fields in geometry of spacetime, or something like that. It makes no sense whatsoever."

I am sorry if this was not so clear to you. I said nothing of the sort "fields in spacetime are something else than fields in geometry of spacetime". I simply reminded the audience of what is explained in many general textbooks. Namely that in a general covariant theory there is not fixed spacetime over which the fields are defined, but rather spacetime becomes itself dynamical: it is itself a physical field. I also said that I thought that understanding *this* physical fact in the quantum theory was the key problem of quantum gravity. This, by the way, is precisely the same problem that David Gross has then emphasized in the final remarks of the conference. Even the words Gross employed ("background independence") are the same, and Gross gently reminded the audience that the problem has to be addressed in string theory as well. In fact, I think that if string theory research focused on the problems that David Gross pointed out at the end of the conference, I myself would consider it far more interesting scientific theory.

You write: "OK, why loops? Now, he could just say that they're open Wilson lines connected by gauge-invariant vertices. People in the room know how to calculate 4-loop terms in things like Wilson lines. Instead, he wastes the time of the auditorium (and mine) by confused presentation of some undergraduate stuff. Instead of saying what he means in one sentence (every other speaker would need roughly 5 seconds for this stuff - someone only 1 second which is too fast), he goes through basic lectures of lattice gauge theory. He is either unaware of the word 'Wilson loop' or thinks that people around don't know what a 'Wilson loop' is. How dumb this guy must be? Let me omit these trivialities."

Perhaps it would be easier to communicate if we listened to one another. In fact, I went into details in order to avoid the confusion that you are making here. The loops I am talking about are *not* the Wilson loops you mention. The Wilson loop you mention are vacuum expectation values of the holonomy operator. The loops of LQG are eigenstates of the electric field operator, with eigenvalue concentrated on the loop itself (which Wilson loops are not). It is precisely to avoid this confusion that I gave the construction of the LQG loop states within the easy lattice context. I am sure that, if instead of assuming you knew everything, you had listened with a bit more care, you would not have fell into this mistake.

You write: "He continues with some elementary stuff about "connections" and "Ashtekar variables". I am convinced that most people in that room have heard about these things already."

Mmm. I do not remember having talked about that, except in the single sentence 'We use the Ashtekar formulation of GR.', which I did not elaborate upon.

You write: "Sorry, I have heard this very same stuff about 15 times already; they think that by constant repetition, they can imprint some nonsense to someone's or everyone's head. Except that this is not how it works in science."

I agree with this. I apologize with the audience if people felt I was repeating well known things. But, Lubos, maybe the majority of the audience have not spent all the long hours that you have spent reading all LQG reviews.

You write: "Childish slides about "loops" and "strings" being both 1-dimensional follow."

This is right; the slide with the comparison loops/slides was a bit childish (explicitly so: I introduced it as a 'cartoon' comparison). I thought it helped bringing across the main point about the *difference* between the two, and about background-independence.

You write: "together with wrong statements that he can define the volume operator on his Hilbert space. It's known that you can't, it's singular (unlike the areas)."

No. The volume operator is well defined.

You write: "He also says a lot of wrong statements about the finiteness of the Hamiltonian. See e.g. Nicolai et al. 2005, the most cited LQG paper in 2005, that explains that these things cannot be well-defined (without an infinite number of continuous ambiguities)."

There are detailed responses to the criticisms raised by that interesting paper, and they can be found online. See for instance Ashtekar's "Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions"  arXiv:0705.2222, and Thiemann's "Loop Quantum Gravity: An Inside View" hep-th/0608210.

You write: "When he tries to talk about the path integral (spin foam in his case), he spends several sentences about Feynman's thesis, apparently assuming that the participants have probably never heard about the path integral. His talk is clearly not addressed to experts of any kind and he has clearly no idea what the physicists in the room are doing, not even approximately."

Again, perhaps if you had listened you would have understood better. What I tried to say in few sentence was (obviously) not what was in Feynman thesis, but what is *different* from that case: for instance the fact that here there is *no* evolution operator here, that the graphs are formed by surfaces and not by lines... So, probably in this slide I went to fast, not too slow. I had only 1/2 hour.

Then your criticisms tend to become a bit less detailed: " 'Loop cosmology' is mentioned as an 'application' of this pseudoscience. ... The usual misconceptions ... Untrue statements about black hole entropy are added ... These people are simply liars... "

I am not sure if these comments demand a rational reply. Something with more ground follows.

You write: "The infinite-dimensional dependence on the cutoff remains both in LQG and loop cosmology; it is only translated to the infinite-dimensional uncertainty of the Hamiltonian, just like in any other case of brute force cutoff regularization."

I do not see how this applies to LQC. This (at least in its basic version) deals with a finite dimensional system. Worrying about what you call the 'uncertainty of the hamiltonian' (I think you mean here things like ordering ambiguities), is like saying that quantum atomic physics is ill-defined because I can add any sort of ordering-ambiguity terms to the Schroedinger equation. I think you are confusing the fact that the quantum theory generally fails to be determined uniquely by its classical limit, with the non-renormalizability problem.

In the full LQG context, I agree that the problem you point out is a central problem. But at the moment, it is not the urgent one. What we are trying to define today is *one* well defined, finite, consistent, background-independent QFT with GR as low energy limit, and capable of describing consistently also Planck scale physics. (Perturbative quantum GR with arbitrary renormalization constants does *not* describe Planck scale physics.) These constraints are extremely strong, and the problem today is finding *one* such theory. If we succeed, and if then you can show that there are an infinite parameter space of such theories, at that time I will be happy to address the problem. But extrapolating the experience with background-dependent theories and assuming a priori that there will be infinite solutions to the problem, when we are still in search of one, seems to me just a way of confusing the issue. Background independent physics may be quite different in this respect. A nice example of what I am saying is 3d quantum gravity, where Perez has shown explicitly that the main regularization ambiguities in the definition of the hamiltonian are entirely fixed by the requirement of full diff-invariance.

Let us now get to the question session. I must say that I was very pleased by these. I got by far the largest number of questions in the entire conference, and very good questions also. I confess I was a bit afraid of getting nasty remarks (your style, Lubos) but there was none. Questions were serious and interesting.

You write: "Simeon Hellerman asks what the can Rovelli possibly mean by a "black hole" if he doesn't even have the right low-energy limit (whose solution the black hole normally is defined to be) [...] Rovelli talks about different definitions of horizons ... "

That's right. I referred to the notion of "isolated horizon", which is a way of characterizing a horizon locally, by the properties of the metric on the horizon itself.

You write: "... which is completely irrelevant because he can't apply any definition of the horizon if he can't localize the Einstein-Hilbert limit with the smooth space in his Hilbert space."

No, this is incorrect. An isolated horizon is characterized by certain equations on the metric field. These equations become quantum operator equations in the quantum theory, therefore one can characterize an horizon *directly* in the quantum theory. There is no need to go to the classical limit of a smooth spacetime. This is the beauty of this derivation.

You write: "The second question [by Simeon Hellerman] is about the coefficient 1/4 and its universality (which is known not to be universal); Rovelli only admits that it is an issue.

The question, as I understood it, was about the value of the Barbero-Immirzi. I replied that the *same* value of the parameter gives the right answer for the different kinds of black holes studied (Schwartshild, Kerr, Kerr-Newman...). I admitted that there is much more to understand here.

You write: "Someone else says that Rovelli is in a topological phase ..."

It was Luis Alvarez-Gaumé. In fact, I did not give a good answer to this question. I missed the word "phase" in the question and understood that Luis was saying that General Relativity must be "topological". So I answered with a small lecture about the difference between topological theories (finite number of degrees of freedom) and diff-invariant ones (infinite number of d.o.f.). Later I asked Luis privately what he meant, and he explained that he wanted to knows whether we were perhaps studying the theory in the 'topological phase', in the sense of the expansion around metric=0. So, my answer should have been simply 'yes'.

You write: " ... - a polite way of saying that he incorrectly treats the groups."

I did not understand from Luis, including in the following conversation that he meant anything of the sort.

You write: " ... In the proper treatment, one gets the gravitons from reducing diff to the Lorentz group; gravitons transform under the latter.

You see, I think that the problem with what you say here is with that "proper treatment". We do not yet know how to formulate a credible complete and physically correct quantum theory of gravity. Something may sound the "proper" treatment to you. But maybe it is not the right path for understanding Nature.

You write: " ... Rovelli tries to prove that a theory that satisfies all the group properties of a topological theory is not topological. ;-) "

The term "topological" can be given different definitions, but it is a fact that 4d general relativity does not have the property of "topological" theories like BF theory or 3d gravity, where the theory has locally (in a finite region) a single solution, and the only degrees of freedom are global.

You write: " ... Michael Douglas asks whether the LQG people have tried to make a contact with the important advances in 3D gravity by Strominger and others (much more solvable). Rovelli has, of course, no idea about the work going on in actual physics, in 3D, 4D, 10D, or any other dimension. He has only heard a remotely related 3D talk by Maloney. So somebody should sit down, he says."

As you correctly say, it is a bit disappointing that the community to which this Rovelli myself belongs didn't immediately zoom in, in trying to understand what Maloney, Strominger and others did. But it is equally disappointing, in my opinion, that the string people who have new results in 3d quantum gravity, didn't pay any attention to the previous vast literature on the subject, and they didn't try any comparison either. This was my answer. The reasons are clear: different communities address problems and use methods that do not fit with the prejudices of the other community, so, the results of one community appear un-interesting to the other community. This is not healthy, I think. In my answer, I was trying to convey the fact that the surprise of the string community about my little attention to the recent 3d results was as great as the surprise of the quantum gravity community hearing Maloney talking about 3d quantum gravity and ignoring the vast quantum gravity literature on the subject.

You write: " ... Someone else asks why they could change the value of the Barbero-Immirzi parameter, from Ashtekar's gamma=i to ln(2)/sqrt(3).pi or something like that (see the quasinormal story on quasinormal modes). Rovelli says that "gamma" is analogous to theta_{QCD} and the value in the quantum theory should be carefully chosen. It's no contradiction, he says. Of course that it is a contradiction because they either obtain a wrong value of the black hole entropy or a wrong Newton's constant at low energies (assuming no divergences and flowing, as he likes to say)."

I do not understand what you are saying here. The Barbero-Immirzi parameter (thanks for correcting my wrong use of "Immirzi parameter") does not affect the classical equations of motion. Changing it might change the relation between low and high energy. Certainly not the low energy physics by itself.

You write: " ... Another question is from a person who knows that LQ cosmology cannot be derived from LQG: it is not a reduction. Rovelli admits it cannot be derived, except for hand-waving (randomly modifying the theory)."

This is not what I said. I said that LQC is quantum cosmology modified with a certain number of ingredients that come from LQG. There is nothing 'random' in this. In a recent work, the LQC dynamics is derived from LQG by first truncating the theory to a spin network with a finite number of nodes, and then using a Bohr-Oppenheimer approximation.

You write: " ... Thank God, it's over. Applause."

I have decided to ignore your sarcasm, Lubos, and only answer the points you have raised. Let me add that I was very pleased with the interaction with the string people, both with many young scientists and with several of the older generation. I found the conference very interesting. In the conclusions, Ooguri said that string theory is (i) a candidate for a fundamental theory, (ii) a model, (ii) a tool and (iv) a language. The impression I got, as an outsider, is that (ii), (iii) and (iv) are interesting, but such a large investment of intellectual energy is only really justified by (i). On this, the most interesting points are those raised by David Gross in the closing remarks: instead of keep developing the part of the theory that appears to be easier to unravel ("looking only under the lamps"), it would be better to face more directly the question of what string theory really is, and wether the candidate is a credible one. Gross invited the audience to address these physical questions, and to try to understand the theory outside a given background. For instance, he invited the audience to stop piling up "proofs" of AdS/CFT (enough of those), and use the correspondence for learning something about the full theory; that is, move *away* from the AdS background and its CFT. These just code a classical solutions, from the point of view of the full theory, and it is time, according to Gross, to move towards true background independence. From the point of view of somebody like me, this is precisely what would make string theory more physically relevant. In LQG, do not have the technical mastership on QFT that I see in the string community (not much is understood about background independent QFT's), but seems to me that in this worship of technical mastership, many in the string world have a bit lost track of the real world. What is of interest is not a theory: it is the world. These are just random thoughts. Maybe LHC will tell us more. Gross, and many at the conference, say they are very confident supersymmetry will be soon found. If they are right, I'll recognize the value of their physical intuition. If not, this confidence will probably sound a bit suspicious.


reader Luboš Motl said...

Dear Carlo,

thanks for your explanations.

1) I am not sure whether you succeeded to explain that we should (or could) construct a "background-independent field theory". The term is pretty much an oxymoron.

If the "background" in the phrase means the dynamical fields of the given field theory, field theories are generally background-dependent or independent depending on the way how we deal with them. It is not their objective physical property: it's a "sociological" label only.

When you talk about a "background" in the stringy sense, as determining the parameters of a field theory, then a field theory is *by definition* background-dependent. If it were background independent, it wouldn't be a field theory. To say otherwise, one would have to redefine the notion of QFT from the scratch, and no one has provided any evidence that such a complete departure from the QFT rules would lead to any sensible theoretical structure.

Also, I don't think you have convinced string theorists that string theory is not everything we know about (this discipline) of physics.

2) I don't know whether the annoyed people formed a "minority" or not. Science is not about majorities and votes. Surely, if there were many people like Alejandro Rivero over there, you could have convinced them about anything. ;-)

But I would insist that the "masters" of their field were almost universally annoyed.

3) The absurdly low pedagogical level you chose was both naive and insulting. The people in the room were not far from being the 400 physics-wise smartest people on this planet, at least many of them. It's just crazy to give a talk assuming that they haven't heard about path integrals. Most of them knew path integrals as high school students.

I also find absurd your statement that top physicists are not "judges" of other people's work. Why do you think so? What does the statement mean? In what sense they're not judges? These people are the crucial ones who follow other people's work and they're implicitly judging every work that is potentially relevant for their work. They have to do it all the time. It's a part of their job.

Also, other people who are focusing on smaller tasks care a lot about the opinion of the people with the big picture, I mean the leaders of string theory. So the latter are not only judges of your or other work but the most important judges that are as close to "spokesmen of Nature [the ultimate judge]" as you can get.

In the very same sense, you might be a judge of other people's work (if you had an idea what the work is) but it is of course not quite guaranteed that your voice would matter as much as David Gross' voice.

4) The talk was about 10 years old. It's not quite true that nothing happened during the 10 years. In fact, many things have happened that have falsified most of the hypotheses you have repeated. I just think it's not honest to neglect what has actually happened in your field in the last decade.

5) The only interpretation of your paragraph about the goal to have a "quantum general relativity plus the Standard Model" is that you claim that no new physics is needed, and you implicitly confirm it again. The phrase "quantum general relativity plus the Standard Model" is a physically meaningless verbal construct. Theories can't be "added" in this way like apples and oranges. The inconsistencies of GR treated in the conventional way are well-known and the impossibility of this "plus" is the whole reason why quantum gravity is nontrivial.

6) You don't seem to like my comment that you said that you thought that the perturbative divergences were illusions, and almost immediately, you essentially repeated that they were illusions. Moreover, you say that perturbative GR is expanded around a "wrong vacuum". What the hell this weird proposition is supposed to mean?

The vacuum in GR is the empty, nearly flat space. It's the correct one. By definition, by experiments, by the very character of the task. Any other vacuum anyone could obtain is wrong, and if a theory fails to get a smooth nearly-flat space limit, it is a completely wrong, unphysical theory. You don't want to create a controversy about this issue, do you?

You say that your bizarre comment about a "wrong vacuum" is taken seriously by many people. Again, irrelevant sociology. I don't know how many people of this kind exist - probably billions of people in the world are confused about these basic things (whether the vacuum is a) empty or b) filled with a liquid of Planckian entropy density with octopi swimming on it: sorry, a) is correct).

I am just saying that the opinion is completely silly and these people shouldn't have received a physics PhD because they have rudimentary ignorance about basic physics and, not seeing what "space" actually looks like, they are really detached from reality.

7) Spacetime itself is dynamical but what this statement means is always the same thing - namely that the geometry, normally given by the metric tensor, is a dynamical degree of freedom. (In string theory, one can show that the discrete data such as topology of the space are dynamical, too.)

The dynamical nature of spacetime simply means that the metric tensor should become "another field" in the effective field theory framework.

There exists no "second" lesson of GR in this direction. In string theory, we've been "dreaming" about a background-independent description for decades but you have apparently misunderstood what this concept means.

It means that one can define the theory in such a way that all regions of the configuration space are equally natural in this language. It surely doesn't mean that the theory should suddenly prevent us from studying particular backgrounds or that people should be ashamed to look at particular backgrounds.

Particular backgrounds have to exist in any theory that has any, even remote change to be relevant for physics. Particular backgrounds are still the "bulk" of physics and the reason why we study theories, sometimes those with complex configuration spaces and many classical solutions.

And it must be possible to expand around these backgrounds. If the physics of a background is understood well - in string theory in the present form, for example - it means that whatever future background-independent formulation will be found, will simply confirm all the conclusions that were found in the conventional background-dependent way.

When Gross or any other person who knows what he is talking about talks about background-independent things, it is only a background-independent description of the same theory, with the same physical predictions for any background that's been understood previously, not a new theory.

8) I insist that the wave functionals in LQG called "spin networks" are gauge-invariant functions of Wilson lines which is the very same thing as the holonomy of a gauge field. (Also, it is not true, as you incorrect say, that the Wilson loop is an expectation value: the Wilson loop is the operator itself.)

They are claimed to have very different properties in LQG than gauge theory (LQG assumes that there is no Yang-Mills dynamics locally) but they are defined in the same way.

You either don't understand what a Wilson loop is, or you don't understand what loop quantum gravity is, or you don't know how to add 2 and 2. Your implicit assumption that I am apparently expected to accept, namely that you have a monopoly on LQG, is strange and unsubstantiated. Sorry, but this kind of "monopolies" is simply not possible to guarantee in science. And it simply doesn't seem that you understand what's going on in LQG too well. See e.g. the most cited 2005 paper about LQG, page 22, so better learn some more LQG: LQG is using functions of Wilson loop observables (with different dynamics).

9) No, the volume operator is not well-defined. Even after many ad hoc steps to eliminate all kinds of ambiguities and singularities, one ambiguity cannot be eliminated by anything, see pages 27-31 here. These ambiguities are related to similar ambiguities that prevent one from defining the Hamiltonian constraint i.e. dynamics. Try to look at LQG somewhat deeper, beyond your kindergarten-level lectures that you began to prefer. Again, I think that Nicolai et al. are much more well-informed experts in these matters - e.g. volume operators - than you are.

10) It doesn't matter that LQC is a "finite-dimensional" system. It is still a regularized 1-dimensional field theory, even in the simplest case, and it still has infinitely many parameters that are needed to define the cutoff dependence i.e. the precise dynamics. In this sense, LQC is as sick as LQG (or any non-renormalizable field theory) itself. But LQC doesn't accurately follow from LQG.

11) Getting a lot of questions of this kind is surely nothing to be proud about, and most questions were politely telling you that you don't know what you're talking about.

Simeon Hellerman told you that it is meaningless to talk about "Schwarzschild black holes" because this object is defined as a particular solution of Einstein's equations, and you don't know whether these equations or others actually govern the long-distance limit if one exists (it probably doesn't exist at all).

He formulated it as a question because it was a "question period". But if you misunderstood what he was telling you, it's just too bad.

Similar comments apply to the wrong pre-factor in the entropy. All existing proposals how to calculate the prefactor (correctly 1/4) have already been shown incorrect.

Your comment "I admitted that there is much more to understand here." is as untrue as most other things you say, and I am afraid you must know that. There exists absolutely nothing waiting to be understood here. All these things have been understood and the answer is simply that it doesn't work. This knowledge cannot be unlearned or re-learned.

12) Luis (and Michael Douglas) were both trying to give you freedom to mention some results that could be more relevant for physics. All these people knew that your teaching surely doesn't work in 4D case or higher, so they were trying to convince you to say that what you do could be relevant in 3D or "topological phases" of some theories because they think that you may have a higher chance to say something relevant about these theories without gravitons than about real physical quantum gravity with gravitons (that you can't even derive from any of your favorite frameworks). You clearly missed their point, too, and continued with the nonsensical quasi-topological description of 4D gravity that is simply not topological in any sense.

Your "We do not yet know how to formulate a credible complete and physically correct quantum theory of gravity" is simply untrue. We - at least I or Gross - know roughly 1,000 times more than what you are ready to admit.

13) It is disappointing that you don't read the papers by Strominger, Maloney, and many others about 3D gravity. But the reason why they don't read yours is simply that they have seen enough to think that your papers are probably (or certainly) wrong. Could you please accept that the situation is extremely far from being symmetric? Would you at least agree that unlike you, Gross has at least won the Nobel prize? Also, the papers by Strominger et al. are more valuable, by any kind of objective criteria I can think of, than the papers you want to be treated equally.

14) Your comments about the Barbero-Immirzi parameter are internally inconsistent. If you actually have 1 quantum theory that predicts gravity and black holes, it must inevitably predict both black holes and Newton's constant (in a force between two black holes). Therefore, it is always possible to check whether the black hole entropy is A/4G where G is defined from Newton's force between two black holes. The value 1/4 in the correct theory is fully physical and not a result of any convention.

If you redefine Newton's constant by a multiplicative coefficient, and the Barbero-Immirzi parameter is doing nothing else, after all, you obtain a mathematically isomorphic theory with a different scale i.e. different units - so if you rescale the entropy, you also rescale Newton's force, and the factor 1/4 won't be fixed.

Of course, you can't derive Newton's force (not even flat space) from LQG but if your comments about the lack of divergences were true, then the Newton's constant governing the low-energy limit would have to be the same one that was inserted, i.e. gamma would have to be one (just like if you naively add hats above classical equations).

Once you decide that the low-energy limit will come with a different value of gamma, it means that there is a nontrivial "flow", just like expected, and there is no reason to expect that the long-distance limit will be governed by Einstein's equations (upon a smooth space) at all.

15) LQC is completely random, has nothing to do with cosmology, cannot be directly derived from LQG, and still has infinitely many undetermined continuous parameters.

Best wishes
Lubos

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