Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

Abstract

We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the solitonic D4 brane and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have different realizations of the Z N centre symmetry and cannot be identified. We propose an alternative gravity dual of the confinement/deconfinement transition in terms of a Gregory-Laflamme transition of the soliton in the IIB frame, where the strong coupling continuation of the deconfinement phase of YM4 is a localized D3 soliton. Our proposal offers a new explanation of several aspects of the thermodynamics of holographic QCD. As an example, we show a new mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The issues discussed in this paper pertain to gravity duals of non-supersymmetric gauge theories in general.

Transition temperature(s) of magnetized two-flavor holographic QCD

“…There are moreover some subtleties concerning the inclusion of flavor branes, but the end result for the ðT; LÞ phase diagram (seeFig. 10of[24]) gives a qualitatively similar result as the ''old'' SSM. Based on this observation, we can expect that qualitative features of the eB dependence of the chiral transition temperatures are not unlikely to be similar in both backgrounds.…”

“…The chiral transition temperature T ;' is the temperature for which ÁS ' becomes zero [23], with ÁSðu 0 ; eB; y T Þ ¼ action [-shape À action straight : (24) The correspondence between u 0 and L in the deconfined phase is modified into (again suppressing the flavor index here)…”

“…Let us remark here that in[24] some problems concerning the identification of the deconfined phase with the black D4-brane background were discussed, and instead a different background was proposed, namely a localized D3-soliton geometry. To make calculations of the critical temperatures feasible, it is, however, necessary to consider a high-temperature approximation of that background.…”

Holographic QCD with dynamical flavors

“…It has been claimed in [17] that the black hole solution is not smoothly connected to the deconfined phase of pure YM in 4d for λ4 1. The "correct" background in this sense is not explicitly known.…”

“…17 In the dual frame, the metric is asymptotically AdS, so one can figure out the counterterms as the standard volume and GH ones on that background. The resulting counterterm boundary action (already uplifted back to 8d) 17) can be written in terms of covariant pieces in the induced boundary metric in the dual frame. Going back to the original metric and adapting everything to the smeared case, the resulting counterterms read In order to cancel the divergences in the probe D8 action (4.16) we have to choose…”