Year: 2026
Type: article
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 $位$ 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 $\sqrt位\,T$ 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 $1/蔚$ poles. The remaining renormalization-scale dependence is fixed by the one-loop beta function. The expansion reproduces earlier results through order $位^{3/2}$, and the order-$位^2$ term is new.
DOI: 10.1103/6x79-kw1b
Authors: Ubaid Tantary, Qianqian Du
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G59735530
OpenAlex ID: W7223214344