What is the gravity dual of the confinement/deconfinement transition in holographic QCD?

TL;DR

This paper challenges the traditional gravity dual of deconfinement in holographic QCD, proposing a new 'localized soliton' solution that better matches QCD properties and describes the phase transition as a Gregory-Laflamme transition.

Contribution

It introduces the 'localized soliton' as the correct gravity dual of deconfinement, revising the conventional black D4 brane picture in holographic QCD.

Findings

The black D4 brane does not correspond to deconfinement.

The 'localized soliton' better models the deconfinement phase.

The phase transition is a Gregory-Laflamme type transition.

Abstract

We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton", which would be properly related to the deconfinement phase. In this case, the confinement/deconfinement transition is realized as a Gregory-Laflamme type transition. We find that our proposal naturally explains several known properties of QCD.