Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

Abstract

Abstract We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for $$ \mathcal{N} $$ 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 mD, MD, and mq 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 $$ \mathcal{N} $$ 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 Padé 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 ≤ λ ≲ 2 and is in agreement with previous approximately self-consistent HTL resummation results for λ ≲ 6.