Fate of Z(N) walls in hot holographic QCD

TL;DR

This paper investigates the behavior of Z(N) domain walls in hot holographic QCD, revealing their structure, tension scaling, and how fundamental flavors influence the stability of Z(N) vacua across phase transitions.

Contribution

It provides a detailed holographic analysis of Z(N) walls, including their tension scaling and the impact of flavors on vacuum stability in deconfined phases.

Findings

Z(N) walls with large charge are described by D2-branes blown up into NS5-branes.

The tension of these walls follows a Casimir scaling law.

Z(N)-vacua are stable below a critical temperature related to flavor mass, but are lifted above it.

Abstract

We first study Z(N) walls in a deconfined phase of Witten's D4-brane background of pure SU(N) Yang-Mills theory, motivated by a recent work in the case of N=4 SYM. Similarly to it, we propose that for a large wall charge k ~ N, it is described by k D2-branes blown up into a NS5-brane wrapping S^3 inside S^4 via Myers effect, and we calculate the tension by suitable U-duality. We find a precise Casimir scaling for the tension formula. We then study the fate of Z(N)-vacua in a presence of fundamental flavors in quenched approximation via gauge/gravity correspondence. In the case of D3/D7 system where one can vary the mass m_q of flavors, we show that there is a phase transition at T_c ~ m_q, below which the Z(N)-vacua survive while they are lifted above the critical temperature. We analytically calculate the energy lift of k'th vacua in the massless case, both in the D3/D7 system and in the Sakai-Sugimoto model.