Higher Order Corrections to the Hagedorn Temperature at Strong Coupling

TL;DR

This paper derives a general formula for higher order corrections to the Hagedorn temperature in holographic confining gauge theories at strong coupling, combining string sigma-model expansion with an effective approach.

Contribution

It introduces a novel formula that includes sigma-model contributions at next-to-next-to-leading order, validated against numerical estimates for ${\

Findings

Agreement with numerical estimates for ${\cal N}=4$ SYM on $S^3$

Predictions for Hagedorn temperature in ABJM on $S^2$

Predictions for the dual of pure RR global $AdS_3$

Abstract

We propose a general formula for higher order corrections to the value of the Hagedorn temperature of a class of holographic confining gauge theories in the strong coupling expansion. Inspired by recent proposals in the literature, the formula combines the sigma-model string expansion with an effective approach. In particular, it includes the sigma-model contributions to the Hagedorn temperature at next-to-next-to leading order, which are computed in full generality. For ${\cal N}=4$ SYM on $S^3$ our result agrees with numerical field theory estimates with excellent precision. We use the general formula to predict the value of the Hagedorn temperature for ABJM on $S^2$ and for the dual of purely RR global $AdS_3$.