Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory

TL;DR

This paper develops a numerical method to accurately determine effective couplings in a 3D Polyakov line theory derived from lattice Yang-Mills, improving understanding of phase transitions at finite temperature.

Contribution

It introduces a numerical approach to extract improved effective couplings directly from 4D Yang-Mills correlators, enhancing the accuracy of effective theories near phase transitions.

Findings

Effective couplings match strong coupling series up to the phase transition.

Critical coupling $eta_c$ is reproduced within 1% accuracy on $N_ au=4$ lattices.

More couplings are needed for higher $N_ au$ to achieve similar accuracy.

Abstract

We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of the 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling $\beta_c$ is reproduced to better than one percent from a one-coupling effective theory on $N_\tau=4$ lattices while up to five couplings are needed on $N_\tau=8$ for the same accuracy.