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arXiv · 2610.23675

Complete $g^6$ pressure of hot Yang-Mills theory

Keijo Kajantie·Pablo Navarrete·Risto Paatelainen·Leon Sandbote·York Schröder·Kaapo Seppänen·Aleksi Vuorinen
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Abstract

We present the full order $g^6$ term in the weak-coupling expansion of the pressure of hot $\mathrm{SU}(3)$ Yang-Mills theory, resolving a problem that has remained open for more than two decades. To achieve this, we evaluate nine previously unknown nonfactorizing four-loop sum-integrals using the thermal loop-tree duality method with novel local ultraviolet and infrared subtractions, thereby completing the hard-scale contribution to the pressure for general $\mathrm{SU}(N_c)$. Combining this result with known chromoelectric and chromomagnetic contributions, available for $N_c=3$, we demonstrate the analytic cancellation of infrared divergences originating from different momentum scales and obtain the complete $O(g^6)$ pressure for $\mathrm{SU}(3)$. Our result displays quantitative agreement with data from four-dimensional lattice simulations over a broad range of temperatures, providing a stringent test of the dimensionally reduced effective-field-theory paradigm.

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Keijo Kajantie, Pablo Navarrete, Risto Paatelainen, Leon Sandbote, York Schröder, Kaapo Seppänen, Aleksi Vuorinen. 2026-10-16. Complete $g^6$ pressure of hot Yang-Mills theory. https://arxiv.org/abs/2610.23675

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