Counterterms for Linear Divergences in Real-Time Classical Gauge Theories at High Temperature

TL;DR

This paper introduces counterterms for linear divergences in real-time classical SU(N) gauge theories at high temperature, providing a lattice model with auxiliary fields that achieve cut-off independence for IR-sensitive quantities.

Contribution

The authors develop a method to cancel linear divergences using auxiliary fields, enabling more accurate lattice simulations of high-temperature gauge theories.

Findings

Counterterms effectively remove linear divergences.

Lattice model with 6+1D auxiliary fields yields cut-off independent results.

An approximate 5+1D auxiliary field model is also discussed.

Abstract

Real-time classical SU($N$) gauge theories at non-zero temperature contain linear divergences. We introduce counterterms for these divergences in the equations of motion in the continuum and on the lattice. These counterterms can be given in terms of auxiliary fields that satisfy local equations of motion. We present a lattice model with 6+1D auxiliary fields that for IR-sensitive quantities yields cut-off independent results to leading order in the coupling. Also an approximation with 5+1D auxiliary fields is discussed.