Complete g6 pressure of hot Yang-Mills theory
Abstract
We present the full order g6 term in the weak-coupling expansion of the pressure of hot 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 SU(Nc). Combining this result with known chromoelectric and chromomagnetic contributions, available for Nc=3, we demonstrate the analytic cancellation of infrared divergences originating from different momentum scales and obtain the complete O(g6) pressure for 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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BibTeX
@misc{kajantie2026complete,
title = {{Complete $g^6$ pressure of hot Yang-Mills theory}},
author = {Keijo Kajantie and Pablo Navarrete and Risto Paatelainen and Leon Sandbote and York Schröder and Kaapo Seppänen and Aleksi Vuorinen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23675},
eprint = {2610.23675},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23675},
}
RIS
TY - UNPB
TI - Complete g^6 pressure of hot Yang-Mills theory
AU - Keijo Kajantie
AU - Pablo Navarrete
AU - Risto Paatelainen
AU - Leon Sandbote
AU - York Schröder
AU - Kaapo Seppänen
AU - Aleksi Vuorinen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23675
UR - https://arxiv.org/abs/2610.23675
AB - We present the full order g^6 term in the weak-coupling expansion of the pressure of hot 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 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 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.
ER -