One Loop Thermal Effective Action

TL;DR

This paper develops a method to compute the one-loop thermal effective action in quantum field theories with background gauge fields, using the Heat-Kernel approach to analyze thermal corrections and phase transitions.

Contribution

It introduces a systematic calculation of the dependence of Polyakov loops on thermal factors within the Heat-Kernel framework, advancing the analysis of finite temperature effects in effective theories.

Findings

Calculated thermal corrections to Wilson coefficients up to arbitrary mass dimension.

Analyzed the impact of Polyakov loops on phase transition dynamics.

Provided a formalism for finite temperature Coleman-Weinberg potential calculations.

Abstract

We compute the one loop effective action for a Quantum Field Theory at finite temperature, in the presence of background gauge fields, employing the Heat-Kernel method. This method enables us to compute the thermal corrections to the Wilson coefficients associated with effective operators up to arbitrary mass dimension, which emerge after integrating out heavy scalars and fermions from a generic UV theory. The Heat-Kernel coefficients are functions of non-zero background `electric', `magnetic' fields, and Polyakov loops. A major application of our formalism is the calculation of the finite temperature Coleman-Weinberg potential in effective theories, necessary for the study of phase transitions. A novel feature of this work is the systematic calculation of the dependence of Polyakov loops on the thermal factors of Heat-Kernel coefficients and the Coleman-Weinberg potential. We study the effect of Polyakov loop factors on phase transitions and comment on future directions in applications of the results derived in this work.