$\mathcal{N}=2$ supersymmetric Yang-Mills thermodynamics from effective field theory

Abstract

We compute the weak-coupling free energy density of pure four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory through second order in the 't Hooft coupling $\lambda$ at finite temperature using effective-field-theory methods. The contribution from the hard scale $T$ is obtained from massless three-loop vacuum diagrams in the full theory, and that from the electric scale $\sqrt{\lambda }T$ from a two-loop calculation in the dimensionally reduced three-dimensional effective theory. In contrast to $\mathcal{N}=4$ SYM, the theory is asymptotically free: the coupling-renormalization counterterm, together with the EFT unit-operator counterterm, cancels all $1/\epsilon$ poles. The remaining renormalization-scale dependence is fixed by the one-loop beta function. The expansion reproduces earlier results through order ${\lambda }^{3/2}$, and the order-${\lambda }^2$ term is new.

arXiv comment13 pages, 7 figures; version accepted for publication in Phys. Rev. D. This work extends the finite-temperature N=4 SYM calculations of arXiv:2105.02101 and arXiv:2111.12160 to pure N=2 SYM. Reproduced diagram figures are identified and attributed in their captions