Some recent advances in the understanding of ${\cal N}=4$ supersymmetric Yang-Mills thermodynamics

TL;DR

This paper reviews recent calculations of the free energy of ${ m N}=4$ supersymmetric Yang-Mills theory at finite temperature, comparing weak and strong coupling results and constructing an interpolating approximation.

Contribution

It provides a second-order resummed perturbative calculation of the free energy and introduces a generalized Padé approximant to connect weak and strong coupling regimes.

Findings

Resummed perturbative free energy calculated to second order in 't Hooft coupling.

Constructed a Padé approximant interpolating between weak and strong coupling results.

Comparison with prior results enhances understanding of ${ m N}=4$ SYM thermodynamics.

Abstract

The interest in the thermodynamics of supersymmetric Yang-Mills started after Maldacena proposed the duality between string theory on AdS backgrounds and the large-N limit of SYM theories. One of the motivations to study the thermal properties of ${\cal N}=4$ supersymmetric Yang-Mills in four dimensions (SYM$_{4,4}$) is that at high temperatures, the weak-coupling limit of this theory has many similarities with high temperature quantum chromodynamics (QCD). In this proceedings contribution, we review recent calculations of the resummed perturbative free energy of ${\cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions through second order in the 't Hooft coupling $\lambda$ at finite temperature and zero chemical potential. We compare our final result with prior results obtained in the weak and strong-coupling limits and construct a generalized Pad\'{e} approximant that interpolates between the weak-coupling result and the large-$N_c$ strong-coupling result.