Linear growth of the trace anomaly in Yang-Mills thermodynamics

TL;DR

This paper demonstrates analytically that the trace anomaly in Yang-Mills thermodynamics grows linearly with temperature, aligning with lattice results and highlighting the system's strong interactions at high temperatures.

Contribution

It provides an analytical derivation of the linear growth of the trace anomaly, linking it to a temperature-dependent ground state in Yang-Mills theories.

Findings

Analytical derivation of linear trace anomaly growth

Agreement with lattice simulation results

Connection to nonperturbative ground state properties

Abstract

In the lattice work by Miller [1,2] and in the work by Zwanziger [3] a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. These results show the remarkable property that the corresponding systems are strong interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with [1,2,3]