Chern-Simons Number Diffusion and Hard Thermal Loops on the Lattice

TL;DR

This paper presents a lattice implementation of the hard thermal loop effective action to measure the sphaleron rate in Yang-Mills theory, confirming theoretical predictions and previous numerical results.

Contribution

It introduces a novel lattice method using auxiliary fields to simulate the hard thermal loop effective action for topological measurements.

Findings

Results match the parametric behavior predicted by theory.

Quantitative agreement with previous numerical studies.

Provides a new computational approach for topological susceptibility in gauge theories.

Abstract

We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at weak coupling. Our results give parametric behavior in accord with the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with the results of Moore, Hu, and Muller.