${\cal N}=4$ supersymmetric Yang-Mills thermodynamics from effective field theory

TL;DR

This paper calculates the free energy density of ${ m N}=4$ supersymmetric Yang-Mills theory at finite temperature up to second order in the 't Hooft coupling, using effective field theory and dimensional reduction methods.

Contribution

It provides a detailed second-order calculation of the free energy density incorporating both hard and soft thermal scales via effective field theory techniques.

Findings

Free energy density computed up to second order in coupling.

Inclusion of effects from both thermal and electric scales.

Use of effective field theory and dimensional reduction methods.

Abstract

The free energy density of ${\cal N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order in the 't Hooft coupling $\lambda$ at finite temperature using effective-field theory methods. The contributions to the free energy density at this order come from the hard scale $T$ and the soft scale $\sqrt{\lambda} T$. The effects of the scale $T$ are encoded in the coefficients of an effective three-dimensional field theory that is obtained by dimensional reduction at finite temperature. The effects of the electric scale $\sqrt{\lambda} T$ are taken into account by perturbative calculations in the effective theory.