## Thursday, September 26, 2013 ... /////

### Guest blog: on applications of holography

By Andreas Karch, physics professor at University of Washington

Having recently made my first appearance in the comment section of a physics blog about the general question of "what has AdS/CFT done for us lately?", Luboš offered me the opportunity to write a guest post about the general topic of "AdS/anything", which I'll prefer to call "Applications of Holography". This entry will be loosely based on variety of very similar colloquium level talks I've given about this topic in the last two years. While I'll try to keep this blog post mostly free of technicalities, readers interested in a slightly more detailed version can refer to my Proceedings for my talk at the PANIC 11 or to the slides for my talk at STRINGS 12.

First off, let me define what the tool is we are using. "AdS/CFT" or the "gauge/gravity correspondence" or "holography" are different words used for more or less the same interesting set of conjectures. Holography is the statement that a large class of strongly coupled field theories has an equivalent description in terms of a classical theory of gravity (in one higher dimension). The conjecture comes with an explicit dictionary. For any quantity of interest in these field theories we can formulate a classical gravitational problem whose solution gives the desired answer in that field theory. This way holography provides us with a series of solvable toy models of strong coupling dynamics.

By toy models here I mean theories that are not actually realized in nature, but share some important qualitative features with the real thing – just like the famous spherical cow. Studying toy models can be important when addressing the real question is simply out of reach. In this case toy models can provide us with quantitative guidance and important qualitative insights. Ideally, they will help us develop new ways to think about the problem at hand so we can eventually develop new techniques to actually solve the problem thrown at us by nature. I will describe a sequence of examples where holography has been used this way.

What sort of questions in physics are currently outside theorist's ability to calculate? Clearly strong coupling is one complication; our prime calculational tool we have all been raised with since our undergraduate days is perturbation theory. Perturbation theory relies on the existence of a small parameter one can expand in. When interactions are weak, the leading order answers can be obtained by considering a bunch of non-interacting particles move around, and the fact that they do every now and then talk to each other can be taken into account systematically, order by order, in that small parameter. But if there is no small parameter, this method clearly fails. Of course other techniques exist at strong coupling. Lattice gauge theory has been used very successfully to calculate many properties of the strong interactions as described by QCD. By discretizing space and time, we turn the very formal path integral of quantum mechanics into a product of ordinary integrals, basically one for each spacetime point. This is something a computer can calculate. The technical problem is that these integrals are still too many to handle for a cutting edge computer – the way lattice gauge theory is implemented in real simulations is via Monte Carlo techniques, also often referred to as importance sampling. In order to calculate the integral, we evaluate the integrand at random points and sum those up. As long as the integrand is real and positive, we can get a good approximation to the full answer by making sure we get a sufficient sample of points in the region where the integrand is largest. This method clearly fails if the integrand can take negative values or is complex. Here the final answer often involves cancelations between different points in the integration region and finite samples give no useful information. This, in a nutshell, is the "sign problem". So when is the weight in the path-integral not a real positive quantity? The path integral measure is $\exp(iS_{\rm action})$, so in general it is complex. For static questions, we can Wick rotate to Euclidean time and the exponential becomes real. This is the realm of lattice gauge theory as it is mostly performed today. Masses, matrix elements, finite temperature thermodynamics are all under control, often with percent level accuracy. But time-dependent phenomena are mostly out of reach. So are even static problems in which we turn on a finite density for fermions, which also leads to a complex weight even in equilibrium. This is especially a problem for simulations of strongly correlated condensed matter systems where of course one wants to have a finite number of charge carriers present. In all these situations, the insights gained from the holographic toy models can be an important first step towards gaining qualitative insights into how a strongly coupled system should behave. Ideally, this will pave the way to formulate new, purely field theoretic tools that will allow one novel ways to attack these old problems.

Before discussing a series of examples of holographic successes, let me spend one paragraph on discussing what sort of strongly coupled theories have holographic duals, as there exist certain misconceptions about this. The first holographic duality gave a solution for $\NNN=4$ supersymmetric Yang-Mills theory (SYM) with a large number of colors $N$ and a large 't Hooft coupling $\lambda = g_{\rm YM}^2 N$. This is a supersymmetric, conformal field theory. Neither of those properties is crucial. Among the zoo of holographically dual pairs, we know lots of examples of confining gauge theories with or without supersymmetry. What all these field theories with holographic dual share are the following two properties: for one, they have to be taken in a limit where the number of local degrees of freedom is large. If they are based on an $SU(N)$ gauge theory, this is typically achieved by a large $N$ limit. This ensures that the theory behaves classically in the right variables. Here the right variables are the gravitational dual. The other property is that the field theory (let us talk about a confining example for concreteness) has a large separation of scales: the lightest spin 1 meson has to have a mass much lower than the lightest spin 2 meson. What this ensures is that the dual holographic theory is based on supergravity, as opposed to a classical string theory. If we could study even classical string theory on AdS space, large $N$ QCD would be solved. But we can't. These days many people calling themselves string theorists essentially study little beyond general relativity – at least as far as applications of holography are concerned. Real QCD has no such separation of scales. The lightest spin 2 and spin 1 mesons come in at $1275\MeV$ and $750\MeV$ respectively. QCD may have a holographic dual, but it is not a supergravity theory. It has to be a full-fledged string theory. In that sense, field theories with a holographic dual (by which I here mean a classical theory of gravity, not a string theory) are toy models.

So what are these toy models good for? Let me give a long list of examples where insights gained from holography have actually have had some impact on how people think about certain physical problems. In this post I will mostly focus on questions motivated by heavy-ion collisions and only briefly touch upon some more recent "AdS/CMT" results later on.

QCD, the theory of the strong interactions, obviously also governs heavy-ion collisions. QCD becomes weakly coupled at very high energies. But around the temperature where nucleons melt into quarks and gluons, QCD still seems to be rather strongly coupled. The equilibrium properties of this strongly coupled soup of quarks and gluons (at least at zero baryon number) can be mapped out with lattice QCD. But a heavy-ion collisions is anything but "static". Two ions (gold/gold at RHIC, lead/lead at the LHC) are smashed into each other to create an exploding fireball of molten quark-gluon liquid. To understand what is going on in the non-equilibrium environment of the rapidly expanding fireball is exactly one of the arenas where holographic toy models can be of some use. Insights that have been gained include the following:

1. Viscosity: The shear viscosity of a fluid determines the force two fluid layers moving past each other exert on each other. More precisely, it gives the force per unit area per unit velocity gradient. As such, it should be measured (in SI units) in $\text{Pa s}$. A more convenient unit is the centipoise ($\text{cp}$), which is $1/1000\,\text{Pa s}$. In these units our favorite fluid, water, has a viscosity of $1\,\text{cp}$, air about $0.02\,\text{cp}$ and honey (depending on your favorite brand) anywhere between $2000\,\text{cp}$ and $10,000\,\text{cp}$. One (in)famous experiment measuring viscosity is the pitch drop experiment from the University of Queensland. It's claim to fame is that it is the world's longest continuously running laboratory experiment. It was started in 1927 and since then has seen 8 drops fall. Despite a video camera being installed after drop 7, no one has seen a drop fall at this machine – the camera malfunctioned at drop 8 (it's slightly younger sister in Ireland recently took a video of a drop falling. Check it out on youtube). One can estimate the viscosity of pitch from this somewhat bizarre experiment at $230$ billion $\text{cp}$ – a seemingly ridiculously large number. So it might come somewhat as a surprise when, after the viscosity of the quark-gluon plasma had been inferred from the experiments at the RHIC heavy-ion collider experiment at Brookhaven National lab came in at about $100,000$ billion $\text{cp}$ (3 orders of magnitude larger than that of pitch), the press release accompanying it announced the discovery of an "extremely low viscosity" that makes this plasma the "most nearly perfect fluid". What this was referring to was earlier holographic calculations by Policastro, Son and Starinets and Kovtun, Son and Starinets finding that the viscosity to entropy ratio takes a universal value ($1/4\pi$) in many holographic models and is larger than that in all fluids known to mankind. So this ratio (and not the viscosity itself) turned out to be the best quantity to measure how well a fluid flows (and to be really small in the quark gluon plasma, but gigantic in pitch). Not only did holography pin point the best observable to use, it also gave a ballpark figure. At this stage, it is almost impossible to go to a talk about heavy-ion physics without a plot that includes the "KSS" bound as a benchmark value. It clearly has influenced strongly how we think about viscosity. The one thing it however is not is, well, a bound. As the ratio becomes large at weak coupling and takes a universal in strongly coupled holographic models KSS thought it may well be a universal bound. We know this not to be true today. And the reason we do is once more holography. $\NNN=2$ SYM based on an $Sp(N)$ gauge theory with a hypermultiplet in the anti-symmetric tensor representation as well as 8 fundamental hypermultiplets has a holographic dual not of the type considered in KSS and violates the "bound", albeit only by a little. So the universal character of the KSS value still stands.

2. Higher order transport: Hydrodynamics is only an approximation valid for long wavelength fluctuations around equilibrium. For very short wavelength, viscous relativistic hydrodynamics becomes acausal. The same happens for example already with the diffusion equation. One time, two space derivatives in the equation imply a non-relativistic dispersion relation where frequency goes as wavenumber squared, so the speed of a wave (frequency over wavenumber) goes to infinity at large wavenumber. This is not a problem conceptually, as hydrodynamics is only supposed to be valid at small wavenumber (that is, at large wavelength). But when modeling hydro on a computer, one needs to tell the computer what to do even at short distances. The acausalities of leading order hydro translate into numerical instabilities. A simple way to fix those is to include higher order terms. Ideally the values of the higher order terms have no impact on the simulation – they are just introduced to stabilize the numerics. If second order terms in a derivative expansion turned out to give important contributions, one obviously should not stop there and the whole long wavelength approximation underlying hydrodynamics would be called into question. To confirm this is not happening, one often varies the higher order transport terms by a factor of $2$ up and down to make sure that the simulation gives the same answers. Of course, varying them over orders of magnitude will eventually have to have effects. So all one needs for a stable running of the code is a rough estimate of what the higher order transport terms should be – an ideal question for holography. In some state of the art numerical simulations of hydrodynamics for heavy-ion collisions (which are needed to, say, extract the viscosity from actual data) holographic values for higher order transport coefficients are routinely used as a default.

3. Anomalous Hydro: Hydrodynamics is non-equilibrium physics (albeit near equilibrium). So understanding the transport coefficients involves real-time correlation functions – the sort of quantities that are challenging on the lattice. It has recently been understood that there is however a small subset of transport coefficients that, in contrast, can be precisely determined even in QCD as they are related to anomalies. These transport coefficients are typically referred to as the chiral magnetic and the chiral vortical effect (CME and CVE). In the presence of a left/right asymmetry in the plasma (which should happen every now and then due to fluctuations) a background magnetic field or a non-trivial eddy current in the plasma will drive an electric current (and hence charge separation). The strength of this effect is uniquely fixed by a simple triangle Feynman diagram and can be calculated in any quantum field theory – be it strongly coupled or not. Whether these phenomena have been or should be seen in heavy-ion collisions is a topic of active debate. The biggest unknown is that we do not understand how large a charge asymmetry one should expect from event-to-event fluctuations. But theoretically the field theory derivations of CME and CVE are extremely clean and insightful – we have learned something about transport in strongly coupled theories that is universally applicable. More recently, these two effects have even been claimed to be potentially relevant in condensed matter systems as well. The so called Weyl metals are conjectured materials that are governed by chiral fermions and hence anomalies. Consequently, they would exhibit the anomaly driven transport phenomena as well. These days one can tell this whole story without any reference to holography. Purely field theoretic arguments (postulating existence of a entropy current or, alternatively, postulating existence of an equilibrium configuration in non-trivial but static backgrounds) can give a complete derivation of both CME and CVE. But the fact that especially the CVE is intrinsically tied to an anomaly was first uncovered using holography. The CVE was found to be uniquely fixed in terms of a bulk Chern-Simons term – the holographic manifestation of anomalies. This came as a complete surprise, but it motivated researchers to look for a connection, which eventually was established. To me, this is really one of the prime examples of how holography should work. We learn something new and surprising about strongly coupled systems using the holographic toy models, which then motivates us to learn something new about the real world using more traditional techniques.

4. Energy Loss: one of the most important probes of what's going on inside the quark-gluon plasma are energetic probes. Sometimes, in the collision of two nuclei that created the quark-gluon plasma there will be isolated collisions of partons (quarks or gluons inside the incoming nuclei) that create a pair of particles with energy much higher than the typical thermal particle in the fireball. How these jets travel through the plasma and lose energy to it can provide a great probe of the plasma properties. One good quantity to calculate theoretically is the stopping distance as a function of energy. In all weakly coupled plasmas (including standard electro-magnetic plasmas) the stopping distance goes as the square root of the energy times a coefficient, the jet quenching parameter, that depends on the details of the theory. Early efforts in understanding jet energy loss at strong coupling have gone into trying to understand this jet quenching parameter. But what has become clear from the holographic toy models is that the change to strong coupling has much more severe consequences – not only the prefactor changes, but in fact the power law itself changes. Instead of $E^{1/2}$, we can get a completely different exponent like $1/3$ or $1/4$. How well this compares with data is something that isn't clear yet. The important point here however is that holography helped us to even understand what the diagnostic of strong coupling should be – a change in power law. Whether the jet interacts weakly or strongly with the plasma doesn't just depend on the plasma, it also depends on the energy of the jet. Asymptotic Freedom of QCD guarantees that at sufficiently high energies the coupling will become weak. The irony of this is that as far as seeing strong coupling in jet physics is concerned, the LHC is a worse experiment than it's predecessor. The LHC generates much higher jet energies and perturbatively inspired models seem to be doing a decent job of explaining the data – even though the final verdict on whether we've really seen the crossover into a weakly coupled regime is certainly still out. At RHIC energies there seem to be some clear indications however that the power laws have to be changed.

5. Far from equilibrium physics: "Strongly coupled far from equilibrium" for a long time has been synonymous for "impossible to calculate, ever". This has certainly changed with the advent of holography. Of course non-equilibrium physics is hard, even when one has a classical gravity dual. But it's possible. One is basically studying the time evolution of a dynamical bulk space-time where injection of energy leads to the formation of a black hole. This is a tricky numerical GR problem. But ever since my local colleagues, Paul Chesler and Larry Yaffe, have been able to demonstrate that this class of problems is substantially easier than traditional numerical GR problems like black-hole mergers, there has been a small industry of people studying non-equilibrium dynamics this way. The verdict is still out on how much we will learn from this. In heavy-ion collisions, perturbative estimates on how soon hydrodynamics should be an approximate description have been way off – the system behaves hydrodynamically after a much shorter time (less than $1\,\text{fermi}/c$) than anticipated. Can this happen in a strongly coupled plasma? Yes, it can. Holography tells us that. But the more interesting questions are what to do with the wealth of numerical data we know have available on strongly coupled non-equilibrium physics thanks to holography. What are the right questions to ask? How to organize the evolution? I would expect many interesting papers in this area in the next two years. The LHC also gave us a recent experimental surprise in this direction: apparently in some fraction of proton on lead collisions, where participants collide head on and produce lots of particles, the system seems to behave like a fluid just like in lead/lead collisions. Intuition from perturbative studies certainly would have told us that such a small system should not behave like a hydrodynamic system – interactions don't have enough time to make the particles talk to each other before they fly apart. How large does a strongly coupled system have to be before it can behave as a fluid? This sort of qualitative question is definitely within reach of holographic methods. Something else that will happen is that people will develop an understanding of how the points discussed earlier, in particular jet energy loss, will be affected by the strongly time dependent environment in a heavy-ion collision.
Let us move on to the set of holographic calculations that have been done with condensed matter applications in mind. In most condensed matter systems, we start with a very simple quantum mechanical Hamiltonian. A fixed number of non-relativistic particles interacting via Coulomb interactions. But it is this Coulombic electron/electron repulsion that makes condensed matter physics hard. It is in size comparable to the interaction of the electrons with the lattice of ions, so it can not be treated as a small perturbation. Every physics major should have seen the solution to Schrodinger's equation for the Hydrogen atom. This is one of the most important results in basic quantum mechanics. But already helium is too hard. If we ignore the electron/electron repulsion, it's just hydrogen all over and we simply "fill up" the energy levels. But it is the electron/electron interaction that ruins this.

Given that two electrons is already too difficult, one may wonder how one should ever hope to say something meaningful about $10^{23}$ electrons in a solid. The basic principle of how people made headway on this question is what we in particle physicists call effective field theory. The idea is that the low energy excitations that govern the transport properties of the solid could be weakly coupled even if the underlying degrees of freedom are not. To pin down the properties of the material, one needs to guess the right low-energy degrees of freedom and then write down the most general action for them consistent with the symmetries of the underlying Hamiltonian (and state). So what could the low energy degrees of freedom be? One natural guess is that one obtains weakly interacting fermion "quasiparticles" with the charge of an electron, but with a finite lifetime and a different mass. These fermionic quasiparticles form a Fermi surface at finite density and weakly scatter off one another. This simple guess forms the basis of Landau's incredible successful Fermi liquid theory. One can even show that in this case the interactions become weaker and weaker as one goes to lower energies – the Fermi liquid is an attractive fixed point. If weakly coupled fermions are one answer, surely weakly coupled bosons could also happen. Sure enough, that is Landau's theory of phase transition, where the relevant low energy degree of freedoms are weakly coupled bosons, fine-tuned to low mass by the vincinity to the phase transition point. But we know experimentally that this can not be all. Materials exist, most prominently high $T_c$ superconductors, that fit neither of the two paradigms. So what other possible low energy phases could be realized in a strongly coupled theory? This is once more an ideal playground for holography as one can address this question already at the level of toy models. Already several novel phases have been constructed, most prominently the "holographic non-Fermi liquids" which can be understood as a Fermi surface coupled to a conformal field theory. But there are many more exciting developments. If there is interest, I'd be happy to describe them in another post (or let Luboš pick another guest blogger to do so).

Let me summarize with my prediction where the field is going. As I hopefully made clear, holography is a powerful tool, but it also has its limitations. Everything is calculable about field theories with holographic dual. This is very unusual in physics and provides a great tool for developing concepts and testing basic ideas. But being all about toy models, it is insufficient to give quantitative descriptions of nature. So ideally we will need to take the lessons learned from the holographic toy models back to the real problem, developing new approaches that incorporate the lessons learned in holography. I think that holography will be a crucial tool that will be with us for quite some time to come, but it is one out of many. I always tell my students that they shouldn't expect to be as lucky as me and count on building a career mostly built on using holography. They need to understand "holography and ...". I anticipate that more and more researchers will appreciate the power of holography and will incorporate it as one of the available tools in their repertoire – but it is clearly not a cure-all that will solve all open problems in theoretical physics.

#### snail feedback (19) :

Andreas Karch,

Thank you very much for this update.

If the qgp is attributed to a location in the collision process(cosmic particle collisions), how would decay products be derived?

So, the microscopic blackhole while quickly dissipating, leaves an energy valuation representing decays products from the collision itself. Would we not say that we have to a degree understood something about microscopic black hole creation in concert with QGP science?

Thanks for this nice post.

Regarding the large ’t Hooft coupling has anyone tried with some broken enough phase of Vasiliev’s Higher
Spin Gravity in the bulk? I know that these theories are very hard to handle and people still don’t know that much about them but I was just wondering if such an approach was even considered.

Still, just for the sake of accuracy, I would like to comment that

(I) "(...) So are even static problems in which we turn on a finite density for fermions, which also leads to a complex weight even in equilibrium (...)"

Well, even in such situations LQCD is rescued by reweighting techniques and so called imaginary chemical potential. So, lattice simulations are still the first choice on nearly-extreme conditions when one needs quantitative predictions to fit data.

(II) "Energy Loss/Far from equilibrium physics"

Still a hard task. But, the most straightforward way here to conciliate usual QCD Blast-Wave models to experiments comes from a simple generalization of BG statistics ( http://xxx.lanl.gov/abs/0812.1609 ).

Thanks for the feedback.

NumCracker:

1) imaginary chemical potential is not the same as real chemical potential. One can try to analytically continue back to real chemical potential, but that is only reliable at extremely small chemical potential, mu << T. The most interesting questions (like whether there is a QCD critical point in nature) are not answered by this approach.

2) If you call "the most straightforward" way a model which has, according to the abstract "two set of parameters" to fit the RHIC data, I think this is a really low hanging fruit. Yes, I agree that the data we have is not enough to completely pin down what is going on. This is not holography's problem - heavy ion collisions are messy. Modified power laws work quite well (see 1305.6458). But ok, so do other thinks.

Giotis: Vasilev Gravity is surely not enough to capture small lambda holography. If you look at the degrees of freedom in Vasilev gravity, they are not enough to give you strings. They just account for the string endpoints, not the actual string. This is because you are studying a vector model instead of a matrix model. The gauge invariant operators are QQ instead of QXXXXXXXX........XXXQ where Q is fundamental and X is adjoint. So you would first have to find the right higher spin dual to free SYM (involving and infinite number of Vasilev-like theories interacting with each other) and then try to break higher spin gauge invariance. I don't think anyone has any idea how to do this, even though the idea has certainly been around.

PlatoHagel: If we were to do heavy ion-collisions in a world which is governed by a gauge theory with a holographic dual, you could indeed say that we learned something about black holes. While being able to describe the collision in terms of the field theory, we would know there is an equivalent, better description in terms of a black hole. But in our world, I am not so sure. We know that if QCD has a dual, it's a quantum string theory on a highly curved background. And yes, we then can say we learned something about black holes in that theory. But would we still recognize what we see as a black hole? As the connection between black holes and heavy-ion physics is more qualitative than quantitative, I would not go so far as to say we can use heavy-ion physics to learn about black holes.

Thank you very much, Andreas, for this review written with the hindsight you may afford now.

Schönen Gruss aus Luxemburg! Wir waren vor 15 Jahren mal gemeinsam auf einer Konferenz in Corfu. Freut mich, dass Du der Physik treu geblieben bist.

Thanks, Andreas. Can you please clarify the following basics for me?

"The lightest spin 2 and spin 1 mesons come in at 1275 MeV and 750 MeV respectively."

So the spin 1 meson *is* lighter than the spin 2 meson. How much lighter would it have to be for a gravitational dual (in the usual sense) to exist?

"If we could study even classical string theory on AdS space, large N QCD would be solved."

What's hard about classical string theory? Surely you mean we'd have to solve the quantum string theory and study the right classical limit of it. If that's correct, what is difficult, identifying the right string background or taking the correct classical limit, or both?

Best, Olena

Thanks for this very nice, interesting article :-)!

The introductery remarks above are nicely adding to the answers of a question I once had on Physics SE

http://physics.stackexchange.com/q/69034/2751

because I was confused by the fact that some people said that supergravity is the holographic gravity dual in AdS/something and others said it is string theory ...

Concerning applications to fluid dynamics of more specifically turbulence: Do you think it is possible to obtain a turbulent diffusion paramterization from holographic considerations? I have quite some time ago seen some PowerPoint slides of Johanna Erdmenger, where she some kind of calculated a turbulent diffusion coefficient from gravity. But I did not save the file and now I can no longer find it :-/. Do you have some good references about this?

The comment concerning new phases found exclusively by applying holography is interesting too. Does this mean that with holographic methods one can find new (IR) fixed points of a system, that are not (easy) detectable when doing "ordinary" renormalization group flow calculations?

In case I mix up and misunderstand things too much, I apologize ...

*inaccessible

Thanks again for the feedback.
Olena:
1) In theories with good (supergravity) holographic dual the ratio of the two masses of lightest spin 2 and spin 1 mesons is lambda^(1/4) where lambda is a large parameter. Corrections to SUGRA go as 1/lambda^(1/2). Maybe one can hope that (1.5)^2 is a large number and so a gravity dual to QCD is not entirely unreasonable, but it's certainly not large enough to think of it as a systematic approximation.
2) To solve QCD holographically we need to understand quantum string theory. To solve large N QCD, we indeed only need classical string theory - meaning no string loops. In practice, this still means you need to understand the 2d QFT living on the string worldsheet (classical string theory then means that you only need to study this 2d theory on the sphere, no need to sum over topologies). For strings in flat space, that 2d theory is free and you can find everything there is to know about it in textbooks. For the kind of backgrounds that appear in holography, that 2d theory so far has proven to be untractable.
Dilaton: look at the recent papers by Paul Chesler. He and his collaborators find numerical gravity solutions to turbulent flows, both in normal as well as superfluids. In turbulent flows energy cascades from large to small scales (or vice versa, depending on the dimension). The advantage holographic models have over purely hydrodynamic simulations is that holography is a complete description, including short distance scales. It knows exactly how the energy in eddies eventually dissipates. Their paper on superfluids is one of the very few string theory papers that ever made it into SCIENCE.

Yes, many thanks for the guest blog... too technical for me to follow much, but I use Penrose's suggestion to skim the material anyway--like learning a language.

Thanks Andreas Karch,

As the connection between black holes and heavy-ion physics is more qualitative than quantitative, I would not go so far as to say we can use heavy-ion physics to learn about black holes.

I was attracted to statements like, "When two particles hit dead-on at close to light speed, a small amount of energy greatly concentrates into a tiny space. Do you see this then as more then just a qualitative look by using experimnt to focus in that space of QGP materialization and the after affects of particle decay?

I guess as laymen, I would want to know if it is okay to say QGP is in fact, the first evdience of microscopic black hole creation?

Physicists know that it should take a certain amount of energy—more than the LHC could ever conjure—to make a microscopic black hole. But if gravity is stronger than we think, then the threshold of energy needed could be within range of both the LHC and cosmic-ray collisions with Earth’s atmosphere, says theoretical physicist Steve Giddings from the University of California, Santa Barbara.See:The hunt for microscopic black holes

Andreas, thanks for your very nice guest post, even if it is largely devoted to what our host very recently described as "some - already not too important - problems of the quark-gluon plasma" ;-) I also enjoyed the slides and proceedings you provided as links.

There is trivial typo in your value for the KSS 'bound'; which I know you know is 1/(4 pi). For those who don't think about this every day I would add that this value is in natural units where hbar and Boltzman's constant are both 1; the magic of the KSS result is that even though both the viscosity and the entropy density are calculated in a stringy theory, in the ratio there are no factors of Newton's constant or the speed of light or the string tension or anything else.

I was amused when you noted that the press release announcing the discovery of the (near) "perfect liquid" incorrectly highlights the small value of the viscosity of QGP, rather than the quantity which is indeed small, the ratio of viscosity to entropy density. I participated in the group that drafted the press release, but was not able to get this fine distinction clarified. If I recall correctly, I believe the counter-arguments were that no one would know what entropy density is, and that engineers routinely tabulate kinematic viscosity (viscosity divided by mass density), so what were talking about is something a relativistic version of kinematic viscosity; let's just call it viscosity. (On the other hand, I was able to get the reference to string theory in the release.)

I also struggled with this issue in two other pieces even when I had more control over the content. The first was an item I wrote on Nuclear Physics Highlights for the Department of Energy http://science.energy.gov/~/media/np/pdf/docs/nph_basicversion_std_res.pdf where (with some back and forth with the editors) I called it "the ratio of viscosity to the thermal density, or entropy". Well, this is technically wrong, 'density' should follow 'entropy', but I guess I'm in good company as the same is true in your post ;-). In the Scientific American article I wrote with Michael Riordan (http://www.scientificamerican.com/article.cfm?id=the-first-few-microsecond-2006-05 , yes, there is a paywall), we referred to the viscosity to entropy density ratio as "specific viscosity", which I think is a useful nomenclature.

Again, thanks for your detailed and interesting discussion!

Dear Bill, it was mostly my typo created during TeXification. There was no parenthesis and in the text form, with the extra space, it looked like multiplication. Of course I know that the right constant is 1/(4 pi).

Yeah, Andreas doesn't disagree with you on this Lubos. But as a researcher you have to decide what topic is interesting AND ripe for progress. I see a lot of interesting things to come out of AdS studies in the next 10 years. Strings and unification - not sure how much we currently have to add over the 80s and 90s.

Thanks, Andreas, your point it appreciated here. The peak of the research rate in the stringy unification may look "earlier" than the AdS/applications research.

But I would guess that you will be proven wrong and in the next 10 years, it will be the big picture of ST that will show some new progress, perhaps experimentally inspired.

I understood the point you were making Lubos and agree with it, but I could not resist the tongue-in-cheek remark. At the same time, over the last ten years I've developed an enormous appreciation for both the insights and the many 'applications' coming from AdS/CFT, so I also agree with Andreas in thinking that there is still a lot of perhaps not fundamental but nonetheless interesting applications to be pursued.

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