Thermodynamics of QCD from Sakai-Sugimoto Model

TL;DR

This paper refines the holographic approach to finite temperature QCD using the Sakai-Sugimoto model by incorporating an imaginary baryon chemical potential, resolving previous monodromy issues and aligning holographic results with perturbative QCD predictions.

Contribution

It introduces a method to include imaginary chemical potentials in the Sakai-Sugimoto model, clarifying the deconfinement phase analysis and matching the Roberge-Weiss potential from QCD.

Findings

Resolved monodromy subtlety in the Sakai-Sugimoto model.

Computed free energy as a function of imaginary chemical potential.

Found agreement with perturbative QCD results.

Abstract

Till date, the only consistent description of the deconfinement phase of the Sakai-Sugimoto model appears to be provided by the analysis of [1] (arXiv:1107.4048). The current version of the analysis, however, has a subtlety regarding the monodromy of quarks around the Euclidean time circle. In this note, we revisit and resolve this issue by considering the effect of an imaginary baryon chemical potential on quark monodromies. With this ingredient, the proposal of [1] for investigating finite temperature QCD using holography is firmly established. Additionally, our technique allows a holographic computation of the free energy as a function of the imaginary chemical potential in the deconfinement phase; we show that our result agrees with the corresponding formula obtained from perturbative QCD, namely the Roberge-Weiss potential.