Effective field theory treatment of ${\cal N}=4$ supersymmetric Yang-Mills thermodynamics

TL;DR

This paper reviews the use of effective field theory methods to calculate the free energy density of ${ m f N}=4$ supersymmetric Yang-Mills theory at finite temperature, up to second order in the 't Hooft coupling, simplifying complex perturbative calculations.

Contribution

It introduces an effective field theory approach to compute the free energy of ${ m f N}=4$ SYM at finite temperature, extending previous perturbative results to second order in the coupling.

Findings

Calculated free energy density up to second order in coupling

Separated contributions from hard and soft scales

Demonstrated effective field theory as a streamlined alternative

Abstract

At finite temperature the free energy density of ${\cal N}=4$ supersymmetric Yang-Mills can be calculated using resummed perturbation theory through the order $\lambda^{5/2}$. Effective field theory methods provide a useful alternative approach to streamline these calculations. In this proceedings contribution, I review recent work with my collaborators where we used effective field theory methods to calculate the free energy density of ${\cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions through second order in the 't Hooft coupling $\lambda$. At this order the contributions to the free energy density come from the hard scale $T$ and the soft scale $\sqrt{\lambda}T$. The contribution from the scale $T$ enters through the coefficients in the effective Lagrangian obtained by dimensional reduction and the effects of the scale $gT$ can be calculated using perturbative methods in the effective theory.