Finite Temperature Tunneling and Phase Transitions in SU(2)-Gauge Theory

TL;DR

This paper analytically investigates phase transitions in an extended SU(2) Yang-Mills theory at finite temperature, demonstrating that only smooth second order transitions occur across all parameter values.

Contribution

It introduces a quartic term to the pure Yang-Mills theory and analytically shows that all phase transitions are second order, providing rare explicit solutions.

Findings

Only smooth second order transitions occur for all parameter values.

Explicit analytical solutions for periodic field configurations.

Transition from quantum tunneling to thermal behavior analyzed.

Abstract

A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field configurations are found, which interpolate between the vacuum and sphaleron field configurations. It is shown by explicit calculation that only smooth second order transitions occur for all permissible values of the parameter $\L$ introduced with the quartic term. The theory is one of the rare cases which can be handled analytically.