185. And more about AdS/QCD

Matt Reece from Princeton has kindly agreed to answer to a couple of my questions related to his comment after the interview with Josh Erlich on AdS/QCD. I hope that his answers will be as interesting for you as they were for me. In what follows D. – me, M. – Matt.

D.: You said that chiral symmetry breaking is reduced to a Higgs mechanism in AdS/QCD. Chiral symmetry breaking does seem to be spontaneous symmetry breaking with pions? Goldstone bosons, but what would play the role of Higgs scalar in real QCD?

M.: This is slightly tricky: the bulk Higgs field is dual to the scalar operator , which indeed gets a VEV in QCD. But the scalar excitations in QCD are difficult to understand. In the 5D theory, there is a set of scalar modes arising as KK modes of the bulk Higgs. Unlike some of the other light mesons, there’s no straightforward way to match them to real states in QCD. Probably the thing that should be thought of as the lightest excitation of this operator is the , but in real QCD lots of other scalar operators are around and they mix a lot; scalar glueballs are likely to be heavier, and the lightest scalar pole (the sigma) is probably best thought of as a 4-quark state. But I am not an expert on this and people argue about it….

D.: Can you explain why one needs RR backgrounds with string scale curvature (you are talking about AdS curvature, right?) to get confimenent?

M. I am talking about AdS curvature, but it doesn’t have to be string scale to get confinement – only to get QCD-like confinement. The point is that in models with controlled duals, there is a hierarchy between the lightest (Kaluza-Klein-like) states and the stringier mesons. This hierarchy is absent in QCD; light states are already stringy. So we will need the full string theory if we are to someday understand them from a dual.

D.: The question about your paper ? would you say that there is a phase transition in , fixed that separates regimes of small and large ? Would you expect that QCD or gluodynamics in the large limit does not have a gravity dual?

M.: There is almost certainly no phase transition (I don’t know of any candidate for an order parameter). Since it’s hard to access the intermediate regime in any controlled calculation, I don’t really know what the transition looks like. In the paper we have a toy quantum mechanics model that shows what such a transition could look like if it is smooth. One interesting result of Klebanov, Maldacena, and Thorn (hep-th/0602255) is that in N=4 SYM, the spectrum of states of a static flux tube has an abrupt change at some critical . I don’t know if there can be similar changes in the spectrum of confining theories as you change the short-distance ‘t Hooft coupling. In any case, such a change is not a phase transition.

QCD and gluodynamics in the large limit should have a gravity dual in the sense that they are probably dual to some higher-dimensional string theory with a massless closed string graviton mode that corresponds to the stress-energy tensor of the boundary theory. On the other hand, Einstein gravity is not a good approximation to these theories, because the stringy states are light and play an important role in the dynamics.

D.: Thanks!