N=2 supersymmetric Yang-Mills thermodynamics from effective field theory

2026/07/26 by Ubaid Tantary, Qianqian Du
#hep-th

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Abstract

We compute the weak-coupling free energy density of pure four-dimensional N=2 supersymmetric Yang-Mills (SYM) theory through second order in the 't Hooft coupling λ 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 √λ T from a two-loop calculation in the dimensionally reduced three-dimensional effective theory. In contrast to N=4 SYM, the theory is asymptotically free: the coupling-renormalization counterterm, together with the EFT unit-operator counterterm, cancels all 1/ε poles. The remaining renormalization-scale dependence is fixed by the one-loop beta function. The expansion reproduces earlier results through order λ^3/2, and the order-λ² term is new.

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