The Bulk Channel in Thermal Gauge Theories

TL;DR

This paper studies the thermal spectral function of the energy-momentum tensor in SU(3) Yang-Mills theory to better understand bulk viscosity, revealing thermal modifications at different frequency ranges through combined theoretical and numerical methods.

Contribution

It provides a detailed analysis of the thermal spectral function, including the high-frequency behavior and the impact of an exact delta function, advancing understanding of bulk viscosity in gauge theories.

Findings

Thermal spectral density is non-zero below the scalar glueball mass m.

Significant depletion of spectral density occurs between m and 3m.

The analysis combines sum rules and Monte Carlo data for spectral density constraints.

Abstract

We investigate the thermal correlator of the trace of the energy-momentum tensor in the SU(3) Yang-Mills theory. Our goal is to constrain the spectral function in that channel, whose low-frequency part determines the bulk viscosity. We focus on the thermal modification of the spectral function, $\rho(\omega,T)-\rho(\omega,0)$. Using the operator-product expansion we give the high-frequency behavior of this difference in terms of thermodynamic potentials. We take into account the presence of an exact delta function located at the origin, which had been missed in previous analyses. We then combine the bulk sum rule and a Monte-Carlo evaluation of the Euclidean correlator to determine the intervals of frequency where the spectral density is enhanced or depleted by thermal effects. We find evidence that the thermal spectral density is non-zero for frequencies below the scalar glueball mass $m$ and is significantly depleted for $m\lesssim\omega\lesssim 3m$.