170. Back to AdS/QCD – interview with Josh
HEP-TH/PH — By Dmitry Podolsky on January 7, 2009 at 4:40 pm
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As you may remember, recently Josh Erlich has made a guest blog post about AdS/QCD at NEQNET. I think that the discussion we had after the post is so terrific that it is worth reposting here in the form of brief interview with Josh. Another reason for reposting is that you, guys, did not want to get into nice physics discussion with Josh, while he was still around (he is attending some conf in Argentina now, as I understand). So, here you go (D. – me, J. – Josh Erlich):
D.: Could you explain in a few words for undergrads, what is Son-Stephanov hidden local symmetry model?
J.: The idea of hidden local symmetry rests in the old observation by Sakurai and others in the 1960′s that the rho mesons act a lot like massive vector fields. Bando and others formalized this idea and called it hidden local symmetry. Son and Stephanov in hep-ph/0304182 formulated an extension of the hidden local symmetry models via a deconstructed 5D SU(2) gauge theory, i.e. a 4D 
gauge theory with large k. Thinking of the SU(2)’s as living at lattice sites along a line, there are scalar fields that transform as bifundamentals of neighboring SU(2) gauge groups. When those scalar fields get vevs, the gauge group is broken, and the massive gauge fields are interpreted as 
and 
mesons.
Below a scale set by the vevs, the action can be written as a 5D gauge theory with some background spacetime geometry with two boundaries, latticized in one dimension. In this sense, it’s just like the Sakai-Sugimoto model.
What Son and Stephanov did that’s so interesting is that they explained in this context why AdS/CFT works. Let’s say the SU(2)’s at each of the two ends of the latticized line are originally just global symmetries, but then we weakly gauge them. The gauge fields couple to conserved currents, so we think of these gauge fields as sources for the 
currents associated with the global symmetries of the theory. To calculate the correlator of a product of currents you vary the generating functional, which in the classical limit is 
where S is the action, with respect to the gauge fields. This is precisely what AdS/CFT tells you to do, if you think of the two SU(2)’s as living at the UV boundaries of the 5D spacetime geometry.
Okay, I guess I didn’t really address this to undergrads, but Son and Stephanov explain it better in their paper.
D.: Why QCD behavior can be considered conformal at mass scales below the mass of rho meson (say, between pion mass and rho meson mass)? What is actually the precision of the physical statement that QCD is conformal (scale invariant) at these energy scales (I mean, how much is it scale invariant when compared to experiment)?
J.: QCD is not conformal around the rho mass. Brodsky and de Teramond have argued based on Jefferson Lab data that there is a window of energies a few times the rho mass over which it seems the QCD coupling doesn’t run, so it looks conformal. At very high energies, where QCD is asynmoptotically free, it is also approximately conformal.
In AdS/QCD we choose the geometry to be 
in the UV region because we ultimately do our best to match to the conformal UV behavior of QCD. Precisely where that begins is not important to us, since it just affects the UV cutoff in the model and most observables we looked at were insensitive to the cutoff. Away from the UV we do not want the model to be conformal, but the choice of a slice of is the simplest geometry that is consistent with the UV behavior, so that’s what we start with. It’s just a toy model that really shouldn’t work as well as it does. It seems that the precise choice of geometry away from the UV region does not have a huge impact on the fit to data.
D.: Why, do you think, naive AdS/CFT is so unnaturally good (it minimizes RMS error, as you say) although it corresponds to N=4 SUSY at field theory side and 
? Can it be that if I introduce more parameters (say, some SUSY breaking terms in the Lagrangian), your statement about minimizing RMS error will go away?
J.: For some things N=4 YM indeed does quite well, but it’s certainly not QCD-like. At finite temperature, certain features of models with supergravity duals are relatively universal, like I mentioned in my post, which is probably why even N=4 YM does well for those things. However, N=4 YM certainly won’t get correct anything that crucially depends on running and confinement, like the spectrum.
SUSY and conformal invariance are not important for AdS/CFT. There are many examples of non-conformal theories that confine, with and without chiral symmetry breaking, and have supergravity duals. The Sakai-Sugimoto model is non-conformal and non-supersymmetric, for example. The large-N limit causes some problems, like infinitely narrow resonances, which is definitely not like real QCD.
I’m sure I didn’t do a great job addressing your questions, but let me know if there’s anything else I can try to help with.
The end, so far. So, people, I can’t believe that you don’t questions about AdS/QCD to a real expert 
4 Comments
Here’s a complete newbie question since my knowledge of ADS/QCD is only from a few random talks.
Whats the upside of all this work? I mean, how far do you think we can veritably go with all this before hitting the limits of the approximation (which still seems quasi miraculous).
Related second question. Which do side do you think will get the most longterm benefit? The ADS part or the QCD part? Learning how to deform/tweak ADS with a physical/experimental theory on one side seems very powerful, but unclear to me how much we can learn ultimately about the infrared QCD part beyond getting semi qualitative agreement with things like Regge slopes?
I can’t resist interjecting my own opinions in response to Haelfix, which might not always agree with Josh’s.
In my view, the main upside of AdS/QCD is that it’s a very powerful toy model of nonperturbative QCD. Chiral symmetry breaking is reduced to a perturbative Higgs mechanism; the Gell-Mann–Oakes–Renner relation drops out automatically; the trend that higher dimension operators interpolate heavier states becomes obvious; you can make a nice model of the U(1)_A problem and the eta’ mass; etc. Like any toy model it has its limitations, but it gets a surprising array of things approximately right.
Backgrounds that are actually constructed in string theory have some other nice features that are absent in the more phenomenological constructions (e.g. magnetic charge screening in confining backgrounds gets a simple geometric interpretation in terms of branes wrapped on shrinking cycles).
These backgrounds offer a nice playground for understanding aspects of nonperturbative gauge theory. But they are not giving us quantitative understanding of real QCD, and this is unlikely to ever happen unless we learn how to do string theory on Ramond-Ramond backgrounds with string-scale curvature. Only it that case will there be long-term benefit for the analytic understanding of confinement in QCD. Otherwise, as toy models these are very nice, but it’s important to keep in mind their limitations.
I just noticed these comments. I guess Dmitry wasn’t lying to me when he told me people read these blogs. In any case, I generally agree with Matt’s comments (and not just on this blog). Like Matt, I think of AdS/QCD as just a toy model, and I suspect we won’t learn anything deep about QCD or about string theory directly from these models. However, I think it’s a cute way to recast things we know about hadronic physics at low energies.
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