Finite Temperature Sum Rules in Lattice Gauge Theory

TL;DR

This paper derives non-perturbative sum rules in finite temperature SU(N) lattice gauge theory, connecting susceptibilities to thermodynamic derivatives, highlighting lattice discretization effects, and proposing methods to control errors.

Contribution

It introduces a new sum rule at finite temperature in lattice gauge theory and analyzes lattice discretization corrections affecting thermodynamic quantities.

Findings

Two sum rules previously derived in continuum are confirmed.

A new sum rule relating susceptibilities to thermodynamic derivatives is presented.

Discretization errors can be mitigated by computing susceptibilities.

Abstract

We derive non-perturbative sum rules in SU($N$) lattice gauge theory at finite temperature. They relate the susceptibilities of the trace anomaly and energy-momentum tensor to temperature derivatives of the thermodynamic potentials. Two of them have been derived previously in the continuum and one is new. In all cases, at finite latttice spacing there are important corrections to the continuum sum rules that are only suppressed by the bare coupling $g_0^2$. We also show how the discretization errors affecting the thermodynamic potentials can be controlled by computing these susceptibilities.