𝒩=2 supersymmetric Yang-Mills thermodynamics from effective field theory
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 λ3/2, and the order-λ2 term is new.
Related
- Two-loop HTL-resummed thermodynamics for pure 𝒩=2 supersymmetric Yang-Mills theory
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BibTeX
@misc{tantary2026𝒩2,
title = {{$\mathcalN=2$ supersymmetric Yang-Mills thermodynamics from effective field theory}},
author = {Ubaid Tantary and Qianqian Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.23620},
eprint = {2607.23620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23620},
}
RIS
TY - UNPB
TI - 𝒩=2 supersymmetric Yang-Mills thermodynamics from effective field theory
AU - Ubaid Tantary
AU - Qianqian Du
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2607.23620
UR - https://arxiv.org/abs/2607.23620
AB - 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-λ^2 term is new.
ER -