3-d lattice SU(3) free energy to four loops

TL;DR

This paper presents a four-loop perturbative calculation of the 3D lattice SU(3) free energy using Numerical Stochastic Perturbation Theory, confirming known results and providing new higher-order coefficients.

Contribution

It introduces the first complete four-loop calculation of the 3D lattice SU(3) free energy, including new coefficients and IR divergence analysis.

Findings

Reproduced first and second order results accurately

Computed new third and fourth order coefficients

Identified the logarithmic IR divergence in the fourth order

Abstract

We report on the perturbative computation of the 3d lattice Yang-Mills free energy to four loops by means of Numerical Stochastic Perturbation Theory. The known first and second orders have been correctly reproduced; the third and fourth order coefficients are new results and the known logarithmic IR divergence in the fourth order has been correctly identified. Progress is being made in switching to the gluon mass IR regularization and the related inclusion of the Faddeev-Popov determinant.