## Tuesday, August 19, 2008 ... //

### Strings 2008: Tuesday

First, great news from the world of awards.

Wikipedia pictures above were taken by your humble correspondent

Joe Polchinski (KITP, UCSB), Juan Maldacena (IAS Princeton), and Cumrun Vafa (Harvard University) joined other well-known physicists and won the 2008 Dirac medal for their stringy discoveries. Congratulations! But back to Strings 2008.

See also the main page about Strings 2008 on this blog... The PDF files are also available at the Strings 2008 website

Luis Ibáňez started the Tuesday morning session by a talk about string phenomenology (PDF here). We all believe that string theory unifies gravity and particle physics but can the SM be embedded and can we predict new things? We will have to use the data (LHC, cosmology) to restrict the possible compactifications. He shows the 1995 duality hexagon of M-theory and adds some structure in it, insights until 2008 (D3-branes, G2 holonomy, RCFTs etc.). The region outside is now called swampland. ;-)

He distinguishes global and local models - global ones are complete, local ones only care about a vicinity of some point in the extra dimensions. The latter incomplete approach is useful and is pursued by many big shots. (At this moment, the Mac starts to misbehave. Beep beep beep and Ibáňez, as an anti-Ellen Feiss, tries to switch to Windows.) That includes D-branes at singularities.

In mapping the MSSM landscape, he begins with the E8 heterotic orbifolds. Pure MSSM can be obtained, gauge coupling unification is likely. Heterotic Calabi-Yaus follow: Wilson lines needed to break to the Standard Model. It's even simpler to eliminate non-MSSM matter.

In type IIA, one combines intersecting D6-branes with orientifolds. The well-studied orbifold constructions involve Z2 x Z2 but recently people found Z6 examples, too. A problem is SM adjoint matter. Mirrors of these models involve magnetized IIB branes.

About 210,000 type IIB Gepner-like RCFTs have been found to resemble the MSSM. Pure MSSM with no exotics can be found. These models probably correspond to too special points in the space of vacua. In type IIB, one can also consider D3-branes (and probably also D7-branes) at singularities.

Finally, GUTs may be found in local F-theory (type IIB-based) compactifications, following Vafa et al. (as discussed right below Ibáňez's talk). New spectrum absent in normal IIB is possible, including spinorial matter and exceptional gauge groups. The GUT is broken to SM by magnetic fluxes. The picture seems to be rather unique.

A table summarizes the successes of the classes - B-L, absence of exotics, gauge coupling unification, fixed moduli. None of them gets an "A" in realistic Yukawa couplings as of now. So we're "not there yet" in getting the complete SM.

He looks at some landscape statistics - which doesn't mean that he adopts the anthropic selection criteria (calm down, please). He believes that some adjoint matter etc. is only light because we're looking at the orbifold points. We don't know whether low-energy SUSY is "generic". (Well, "generic" is something different than "predicted" by the theory, but OK.) He looks at the Yukawa couplings, stressing that non-perturbative contributions may be crucial. Examples of brane instantons in intersecting braneworlds follow.

Fluxes have been known to fix the moduli for 5 years or so (somewhat bizarre references for this fixing). A better control is obtained in large-volume models with multiple separated Kähler moduli. In type IIA, one can stabilize the moduli without instantons (Kähler and complex structure moduli co-operate). And the bulk of the landscape could be non-geometric.

What is the string scale? When it's 1 TeV, it's cool with all the Kaluza-Klein, stringy, black hole signatures at the LHC. More likely, when it's at the GUT scale, SUSY can be at 1 TeV. SUSY breaking has to be calculated and is not easy.

In string theory, it can arise from closed string fluxes, dynamical breaking in a gauge sector. Also from gravity, gauge, anomaly mediation (and mirage - perhaps natural in KKLT...). They each have advantages and disadvantages. The LHC should tell us something about it here. Type IIB has no Kähler moduli dependence of the superpotential, unlike type IIA.

There are three different very predictive types of SUSY breaking of some kind where all the superpartner masses are determined by one dimensionful (and a few known dimensionless) parameters. Intersecting 7-branes give us a very clear pattern. Stau tends to be the LSP but it can be fixed.

The LHC will tell us something about the string theory vacuum. If low-energy gravity works, great. If SUSY is found, extremely good. The only pessimistic scenario is that only the Higgs is found: the anthropic explanation of the electroweak-Planck gap will gain power. Also, unexpected surprises are possible. In a few years, the hexagon of M-theory will be covered by overlapping new circles of LHC and cosmology constraints - the right class but probably not the right exact vacuum may be located. A very good talk!

Cumrun Vafa mostly uses colorful tablet-PC, partially hand-written (maths and pictures) slides (PDF here). Very readable. (I was fixing his tablet PC as well as laptop once haha.)

He starts his talk about F-theoretical phenomenology by our goal to find the theory of everything. He finds anthropic explanations unsatisfactory while the goal to find the full exact theory hard. To solve the first (anthropic) problem, he prefers to search for the keys under the lamppost ;-). To solve the second part, he has to look for parts: a justification of the "local models" follows.

Cumrun refers to the SM-like sector as "open strings" and the gravity sector as "closed strings". So we focus on the vicinity of the place where the SM lives. One must assume that gravity decouples from the SM: that can be false but it's healthy to try. This assumption implies, for example, that the GUT must be asymptotically free so that gravity may have been postponed to higher-than-Planckian energies by Nature.

Interesting matter-carrying branes must be SUSY-like, i.e. wrapped on 2, 3, or 4-dimensional cycles. He thinks that the higher-dimensional branes are more flexible which is why he chooses 3+4 = 7-dimensional branes, leading him to type IIB.

Another input is a SUSY GUT-like unification. He views the pretty and natural representation theory of GUT to be stronger evidence supporting GUT than gauge coupling unification. Now, gauge groups like SO(10) are easy in type IIB but the spinor seems impossible (much like the top quark Yukawa coupling) so he must go to (va)F(a)-theory, non-perturbative IIB (his brainchild), where all problems are solved. Cumrun is shocked that his cell phone is able to interfere with the microphone or speakers (noise!). I've learned this thing a few months ago (experimentally). ;-)

There's a nice even-dimensional hierarchical structure here: gravity lives in 10 dimensions, gauge fields in 8 dimensions, matter fields in 6 dimensions, and interactions in 4 dimensions (the intersections).

The SO(10) spinor arises from a decomposition of the E6 reps: E6 singularity is needed, requiring F-theory and the "5.10.10" coupling in SU(5) is generated from the E6 structure, too. Now, one can show that the 7-branes supporting the gauge fields must be del Pezzo surfaces because they must be able to shrink, giving you a positive curvature. The surface is essentially unique.

The Wilson lines can't be used to break the GUT symmetry here since the del Pezzo has no cycles. The right Higgs can't exist either because that would correspond to a non-existent deformation of the local geometry. One is forced to use the fluxes. The cycle is determined! It must be mapped to a root of E8.

Geometrically, he has to solve the doublet-triplet splitting problem and the solution automatically solves the proton decay problems, too: quartic terms in the superpotential (from 4-fold intersections) are absent. Predictions for light and heavy neutrinos seem reasonable, plus minus an order of magnitude or so. The mu-terms and SUSY breaking will follow.

The SUSY breaking is very predictive in this setup. Vafa reviews gauge and gravity mediation of SUSY breaking. The Goldstino chiral multiplet (X + theta^2 F) has the F-term. The dimension of F is squared mass. Depending on the value, one can distinguish the the types of mediation. By his philosophy, he wants gauge mediation because gravity is decoupled. But now, B mu term can't be made small if the mu-term is large enough.

So the mu-term must come from a D-term (Giudice-Masiero mechanism), like in gravity mediation. Tan beta is then naturally large, and the small bottom/top mass ratio is thus natural without fine-tuned Yukawa couplings. All scales are then fixed, close to the sweet spot SUSY, and the Peccei-Quinn 7-brane is paramount for SUSY breaking. The PQ symmetry is anomalous and Higgsed by a GS mechanism. String theory allows them a hybrid of Fayet and Polonyi models. The QCD axion arises automatically with a marginally tolerable decay constant, 10^{12} GeV. The good things, like the correct U(1)_{PQ} charges, are obtained from the E6 symmetry, without the extra field-theoretical E6 baggage.

Cumrun is finally able to make extremely accurate predictions for the LHC. The Bino is the lightest superpartner, followed by stau. Tan beta is between 20 and 30 (an unusual value, a bold prediction, indeed). A brilliant talk.

Question: is there a IIA mirror dual? Cumrun is not sure whether it exists at all. Question: how can the instantons be suppressed if you're in non-perturbative regime? Cumrun says that non-perturbative is about "tau" but the suppression is due to large volumes. Another question is answered by "F wedge H is zero".

Cumrun spends his coffee break by off-camera, on-microphone discussions, mostly with Andy Strominger. Those 6 meters in between their offices in Cambridge are probably too many so these questions haven't yet been answered. ;-)

After the coffee break, Alessandro Tomasiello continues with a talk about AdS4 flux vacua (PDF here). Some people are motivated by AdS4 as the starting point for realistic vacua. He is motivated by knowledge of some stringy geometry (theoretical motivation). He will look at AdS4 x CP3. At some point, SUSY may become N=6, an old solution whose CFT3 dual was found recently. He explains how generalized how-flat (generalized complex) manifolds are defined, by the amount of SUSY. The SU(3) structure manifolds - a subclass - is more well-known.

The wedge products still vanish, like in Calabi-Yaus, but the exterior derivatives of J, Re(Omega) don't: they're proportional to the other form. Some bad news about the vacua are mentioned. But there are many of them. ;-) So he's listing various manifolds with N=3 (and N=2, N=1) SUSY, without explaining too clearly what (how complete) the list exactly is. A double-U(1) quotient of SU(3) has a known CFT3 (quiver gauge theory) dual.

A list of allowed topologies (sometimes with several metric per topology) increases a bit when some masses are allowed. It looks somewhat disorganized to me. A moduli space is found to be a line interval but that's an inaccurate artifact of SUGRA because 1) flux quantization, 2) string corrections. Some pictures with the angle whose meaning I missed are shown. Are there many animals of this kind, he asks? Answer: a question mark.

Conclusions: even for simple topologies, there are often infinitely many vacua (with N=3 Chern-Simons CFT3 duals). Question: Michael Douglas wants to defend his statements about the finiteness of the number of vacua, so he points out that if one restricts the size of hidden dimensions, the number is finite. Answer: confirmed.

Timo Weigand talks about D-brane instantons in type II orientifolds, a technical topic that was investigated in a lot of papers during the last year (PDF here). The motivation seemed confusing. But the technicalities have content. D-brane instantons are divided into two groups - whether or not their cycles are inside existing physical D-branes. If they are, they can be interpreted as stringy realizations of gauge instantons. If they are not, they are exotic stringy instantons. A lot of work has been done and won't be mentioned.

First, he counts zero modes on the instantons. They come from open strings that can either end on the same D-brane instanton or two different ones. The first group has some universal modes; the second is typically found near intersections and has phenomenologically interesting couplings.

Superpotential can only be generated by BPS instantons, and not even all of them: two zero modes must be lifted. By picking a transverse geometry or e.g. a flux or ... by interactions in the E-E' sector. (D-terms are contributed to by non-BPS, off-calibrated instantons.) Concerning the latter, the goldstinos are lifted by this E-E' stuff. Now he, somewhat repetitively and off-topic, jumps to the other ways of lifting the zero modes.

He talks about the invariance of the instantons under the orientifold transformation. At some points in the closed-string moduli space, you're forced to choose bound states of instantons. A rather complicated discussion which terms are generated by various bound states of the instantons appears here. Chiral intersections can prevent the instanton action from having any method to lift the zero modes (global constraints, related to index theorems etc.). By looking at lines of marginal (or, later, threshold) stability, one can see that the instantons should be allowed to split etc.

He argues that only certain superpotentials can occur from the D-brane instantons: they should satisfy similar charge constraints as the perturbative terms, except that the balance may be shifted by the charges from the additional zero modes. This stuff has various applications. One of them is SUSY breaking by F-terms: production of Polonyi terms. He tries to construct a full-fledged SUSY breaking scenario. The context is somewhat unclear to me. Question/complaint: Cumrun says that the U(1) and SU(5) couplings should be naturally identified which makes it unnatural to produce the "5.10.10" coupling in Timo's way. Yes.

Stephan Stieberger titled his talk "Superstring amplitudes and implications for the LHC" (PDF here). It's focusing on tree-level multi-point amplitudes, their compact form (e.g. six-gluon disk amplitude), and possible stringy signals at the LHC relevant for QCD jets.

Now, he reviews the MHV-like QCD amplitudes (we know from the twistor industry). The next slides are about SUSY variations of vertex operators. He argues that certain recursive relations for multi-point MHV QCD amplitudes hold to all orders in alpha' in string theory (universal for all compactifications). SUSY Ward identities reduces 6-point amplitudes to simpler ones. Then he wants to get the full n-gluon amplitude in string theory from the "first principles", namely from the correct soft boson limit, collinear limit (factorization), and permutation symmetries.

He looks at various arrangements, e.g. 2 gluons and 2 chiral fermions. The results so far are universal for type I and type II theories. To see some stringy stuff of this simple kind at the LHC, he needs to assume ADD large dimensions. To see the strings, he would look at dijet events and Regge excitation resonances in the s-channel. Well, it would indeed be easy to see the strings if they existed there. Now, the discussion almost looks like Chapter 1 of the Green-Schwarz-Witten textbook. High-precision tests would tell us about the internal shape but he doesn't specify how the reverse engineering is made.

A question: what are you doing with background? Answer: Yes (not clear what he exactly means). ;-) Another question from Kiritsis: why haven't you seen the Z'-like particles at 100s of GeV that would exist for a TeV string scale? Answer: Z' are irrelevant. A small argument explodes. At any rate, I agree with the guy who asks that these models are already excluded.

Ron Donagi started the afternoon session with Heterotic Standard Models, a topic that was repeatedly covered on this blog. The talk began with a technical interlude, namely a struggle involving the screen size of the Apple's PowerPoint (or replacement). The Apple devoured his paper. It was a really good paper. A kind of a bummer. Applause. :-)

Juan Maldacena was ready to jump onto the scene and speak instead about the membrane minirevolution, namely their "ABJM" N=6 supersymmetric U(N) x U(N) Chern-Simons SCFT in three dimensions, generalizing the Bagger-Lambert-Gustavsson theory (PDF here). He wrote the action and demonstrated its classical scale invariance. Then he mentioned that N=3 CS-like (with Klebanov-Witten quartic superpotential) theories are common in 3D. He doubles the supercharges by looking at some R-symmetries.

The theory describes M2-branes proving an 8-manifold with a R8 / Z_k singularity. In detail, two NS5-branes with N D3-branes gives Yang-Mills plus bifundamental matter. One NS5-brane is rotated, we get N=3 YM CS plus bifundamental hypers. Some dualities lead to M-theory with two circles. Two KK monopoles are possible and their intersection is a special kind of hyperKähler singularity. Close to the R8/Z_k singularity, SUSY is enhanced to N=6.

1/k plays a role of the coupling constant: the theory is free for large "k". There is another parameter N, the number of M2-branes, and 't Hooft limit is possible for N/k=lambda fixed and N large. For N=2 and U(2)'s replaced by SU(2)'s, one gets the Bagger-Lambert-Gustavsson theory.

The gravity dual involves AdS4 x S7/Z_k, with a free action. For large k, Z_k "becomes" U(1) and S^7 becomes CP_3 - Tomasiello's talk... When he calculates the thermal free energy, the 3/4 from YM is replaced by 1/sqrt(lambda). He discusses operators - some BMN-like traces as well as 't Hooft operators (postulating a unit of magnetic flux around one point). A bifundamental operator must be added (k of them). The BMN-traces are simply type IIA strings, with no KK momentum along the Z_k orbifolded direction. The others are D0-branes, with a D0 momentum.

For k=1,2 he gets enhanced symmetries, analogous to SU(2)'s at the self-dual radius, in this case ordinary SU(4) and/or an extra center-of-mass symmetry for k=1. Similarly to AdS5 x S5, it seems integrable (classically) and you wonder whether it is an exact statement.

Changing U(N) x U(N) to two different ranks is like adding torsion F4 flux in M-theory. You can't find a Lagrangian that would flow to it. One can try to orientifold the theory, squash the 7-sphere, take more complex quivers, etc. So in conclusions, they have presented a surely interesting theory. He wants to master the 't Hooft operators, decide the integrability, maybe find duals of more general AdS4 vacua, and study the condensed-matter applications (which is likely for their theory than to describe the Universe).

A question why it is a gauge theory or something like that - hard to heard through the noise. Juan didn't quite know the answer. Another question: why would you expect conformal invariance? Answer: SUSY, presence of singularity in the moduli space. Third question: what condensed-matter applications? Answer - two: either 2+1-dimensional systems; or the Euclidean version may be good for critical phenomena. Another question: can you get the Yang-Mills limit (for k=1)? Answer: repeating some BL-G wisdom plus no answer about k=1.

Ron Donagi has another attempt (PDF here). Everything works now (except for the letter "B" at the end of every line). Heterotic Standard Models are the High Country of the landscape (anti-swampland): only 1 item is known right now. They're looking for full global models only. He plans to cover 7 papers, 6 of which included him, one of which is in preparation (with a female co-author).

The playing field is a Calabi-Yau with a SU(4) or SU(5) polystable bundle. Anomalies must be canceled: c2(X)-c2(V)=[M5 branes]. Commutant H in G is the low-energy group, Wilson lines (Z2 for SU(4) or, for SU(4), Z3 squared or Z6) get you to MSSM, 3 generations must exist.

For his favorite SU(5) case with Z2 Wilson lines, he needs a manifold with a freely acting Z2. Xtilde, the larger manifold, is either his favorite fiber product of two del Pezzo surfaces. Or a complete intersection of 4 quadrics in CP7. ;-) His way is the only close to MSSM so he explains the fiber product. It's like a Cartesian product of two elliptic fibrations except that you only take the points with the same location on the two fibers, effectively removing one of them. The manifold has h12, h11 equal to 19, 19, superficially a self-mirror.

Fourier-Mukai transform is used to construct the (Z2-invariant) bundle. Sometimes, monads are helpful etc. The anomaly is canceled either by M5-branes or, preferably, by bundles in the hidden sectors.

Years ago, he expected the model to be the first example among zillions. It unexpectedly remains the only one. So he still finds it ludicrous for him to successfully describe the Universe by his first algebraic geometry construction but the audience is clearly expected to be more optimistic. ;-) My estimated probability that their precise model is right is comparable to 1%. Phenomenological properties seem OK - pure MSSM, R-symmetry preserved classically (stable proton), semi-realistic Yukawa couplings and mu-terms.

There are other models which don't have stable V (Braun et al.). NAHE by Faraggi et al. are mentioned, too. Relaxing one of the conditions expands the landscape hugely. Now he talks about many not-quite-realistic models, including the (51,3) Vafa-Witten model, classified by various groups etc.: large tables with discrete data. A (2-9) free fermionic model is connected to their geometric compactification.

In the new paper, they have 1 construction that may generate a couple of new examples (or not). To summarize, the High Country is small and only has 1 fine representative right now. His plan involves strategies to look for new geometries and bundles. I think they should pay much more attention to detailed investigation of their best model. Stabilization & F-theory duals should be looked at.

In the question period, a participant claims that you can use fluxes to break the group. Another question is answered by Donagi's absent taste to study asymmetric orbifolds and nongeometric models. Another question is what they do with the hidden E8. Initially nothing. Later, it has a bundle on it. Addition to the question: he thinks that if both E8 can be used nontrivially, the High Country expands dramatically, he says. Donagi would like to know details.

Neil Lambert - now a part of Bagger-Lambert - will unsurprisingly talk about multiple M2-brane Lagrangians, the membrane minirevolution he helped to spark (his PDF is here). He can't enumerate all the work here - there has been too much. M-branes are hard, there's no dilaton to make it weakly coupled. The Lagrangian description is not known - a point to be challenged (although Juan's challenge has probably been superior by now).

For a stack of M2-branes, the SUSY variation of X is universal - schematically epsilon times psi. The variation of psi is epsilon times partial(X) plus a cubic term in X, in this case, times epsilon. So he's led to a 3-algebra (something with a triple product). Historically, he reviewed his steps to construct the Lagrangian. Click at "membrane minirevolution" above to see more comments about this construction; I won't repeat it here.

The algebra closes if the mutated Jacobi ("fundamental") identity holds. The Lagrangian eventually has the right symmetries, including parity (that was hard). The SU(2) x SU(2)-based 3-algebra, the simplest example, is explained. There are infinite-dimensional examples (equivalent to an M5-brane?). Their simple theory has R8 x R8 / D_{2k} for the two membranes. For k=1, it only differs by a O(4) vs SO(4) difference. For k=2, it works. For higher k, the orbifold action looks weird: the coordinates of branes are nontrivially mixed/rotated together as a doublet. ;-)

The origin of N^3 is hinted. Enhanced symmetry (classically) appears when the branes are collinear, not necessarily coincident. When the 4-index structure constants are non-antisymmetric, there are infinitely many examples but there are no gauge-invariant observables. The status of the non-unitary, indefinite algebras is not yet settled while "ABJM" (see Maldacena above) is where the field has gone. Various other modifications - like "ABJ" with torsion - are mentioned.

For SU(4) x U(1) smaller R-symmetry replacing SO(8), they're led to new symmetry conditions for the structure constants. They're Riemann-tensor-like symmetries, with an extra complex conjugation for the exchange of the pairs of indices. You find an infinite class of 3-algebras here, with explicit "XZ*Y - YZ*X" formulae for the 3-product. Many more papers with new groups, classifications of models etc.

To conclude, they constructed a unique (but k-labeled) theory for multiple M2-branes. The only example of a maximally supersymmetric gauge theory without gauge bosons is it. ABJM is the interesting broader class. He bets - but can't prove - that the N=8 theory is relevant for M-theory even above k=2. Can we see the 3/2-th power in the entropy? Vague proposals.

Do we really need the 3-algebras? You're right, we don't. ;-) But they have the same classification. But the physical fields, scalars and fermions, don't directly see the 3-bracket. His mother is one of 2 people who believes that something here is interesting ;-), thank you. Some questions. The first had a vague answer. The second, about coupling to SUGRA backgrounds, is also unclear. Many other questions are asked (Neil is a great person to answer questions), for example: why can you only describe 2 branes? Neil thinks that it just seems to be the only number for which this theory works (some special features of the orbifold).

To make the topics diverse, Sunil Mukhi - who is also a blogger ;-) and who is blogging from the coolest place in the Universe - speaks about the membrane minirevolution, too (PDF here). He will try to minimize the overlaps. He will describe roughly 3 papers, including the D2-branes from M2-branes that we reported at the beginning of the minirevolution.

Sunil is funny. There was an agreement that it (M2-brane Lagrangian) couldn't be done because it was not done. But now, once it's been done, we agree it can be done but it should be done better. In France, they have "brane" wines - a bottle shown on a picture. ;-)

His interest is in the extension of SO(7) to SO(8) and his classification of the known algebras is from a somewhat different angle. Unlike other speakers, he finds the indefinite 3-algebras interesting and he will focus on them. A new gauge symmetry manifestly removes the bad ghosts (and some good things, too). Some overlap with "ABJM" and "ABJ" is mentioned. New excuses why the theory is not known for N above 2: it would be strongly coupled, anyway (and the classical Lagrangian not overly useful).

As explained in the "D2 from M2" article linked above, Sunil tells us how the gauge field becomes dynamical - a new kind of Higgs mechanism. How is it possible that Higgsing makes a compactification? Because of higher corrections in 1/vev. The decoupling is only for infinite vev (like in our deconstruction paper with Nima et al. that Sunil mentions: yes, the derivation of the cylinder limit from the cone, and the stringy duality derivation from the quiver, was my work in the paper). In this present setup, the large vev can be replaced by a high level (order of the orbifolding group).

Finally, something that Sunil found pretty, then ugly, and now again pretty. ;-) The Lorentzian algebras. He adds some B-wedge-F terms to the Lagrangian. These theories violate Juan's wisdom that one can make a theory classical by adding a large classical prefactor to the action: if you add one, you can get rid of it by a field redefinition. The Higgs mechanism works in their picture but it works too well. ;-) More precisely, one gets the exact Yang-Mills (a reformulation? that seems disappointing).

To show the equivalence, non-Abelian dNS symmetry produces a non-dynamical gauge field: harmless. The duality works, by integrating out something (B?), and he explicitly constructs a Lagrangian where the SO(8) symmetry emerges except that it should also act on the coupling constants. To summarize, after some exercises, one can rewrite the N=8 Yang-Mills in a (Lorentzian) 3-algebra friendly way. But the superconformal and SO(8) symmetry is broken immediately when the vevs etc. are added.

Last two minutes dedicated to extra topics about the Lorentzian algebras: can one generalize the steps above with alpha' corrections added? Will the 3-algebra structure survive the stringy additions? So he adds a lot of F^4 terms and those of the same order. After the procedure, the result is still SO(8)-invariant! The enhancement works to all orders. To conclude, there's been much progress for multiple M2-branes but not a complete progress. A funny picture at the end.

For the third talk about the same topic, it was an extremely refreshing and original talk! ;-) Question: is the equivalence classical or quantum? Answer: it was done classically. Juan: what's the Goldstone boson for the broken conformal symmetry? It's not there - the field must be constant. New question: make D2-branes in a varying dilaton. Will the X8 vary? Sunil sees no problems but warns that the variations of other fields can't be forgotten.

Tuesday talks are over. The text above is too long, too few people will read it, and I won't be fixing the typos, sorry.
Monday, Tuesday, Wednesday, Thursday, Friday