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

Abstract

At finite temperature the free energy density of $\mathcal{N}=4$ 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 $\mathcal{N}=4$ 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.

Comments: 4 pages, 3 figures; Contribution to the 2022 QCD session of the 56th Rencontres de Moriond