Two-loop HTL-resummed thermodynamics for N=4 supersymmetric Yang-Mills theory

TL;DR

This paper calculates the two-loop HTL-resummed thermodynamic potential for N=4 SYM, providing gauge-invariant results and comparing them with known weak- and strong-coupling limits, as well as previous approximations.

Contribution

It presents the first two-loop HTL-resummed thermodynamic functions for N=4 SYM with a self-consistent determination of mass parameters, improving the understanding of thermal properties.

Findings

Quantitative agreement with weak- and strong-coupling limits.

Reliable approximation for entropy density for coupling λ <~ 2.

Consistency with previous HTL resummation and Padé approximants.

Abstract

We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for N=4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using only simple vacuum energy, gluon mass, scalar mass, and quark mass counter terms. The HTL mass parameters m_D, M_D, and m_q are then determined self-consistently using a variational prescription which results in a set of coupled gap equations. Based on this, we obtain the two-loop HTL-resummed thermodynamic functions of N=4 SYM. We compare our final result with known results obtained in the weak- and strong-coupling limits. We also compare to previously obtained approximately self-consistent HTL resummations and Pad\'e approximants. We find that the two-loop HTL resummed results for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 <= lambda <~ 2 and is in agreement with previous approximately self-consistent HTL resummation results for lambda <~ 6.