Gauge Choices, Infrared Pitfalls, and Thermal Effects in Effective Potentials

TL;DR

This paper investigates gauge choices and infrared issues in effective potential calculations, demonstrating how the Heat Kernel technique improves gauge independence and IR behavior, especially at finite temperature, with implications for cosmology and particle physics.

Contribution

It introduces a method using the Heat Kernel approach to enhance gauge independence and IR behavior in effective potential calculations, including at finite temperature.

Findings

Gauge independence is improved using the Heat Kernel technique.

Infrared divergences are mitigated in the Landau gauge.

Finite temperature effects are incorporated with extended gauge independence.

Abstract

The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge-dependence of the effective potential. Furthermore, in theories with spontaneous symmetry breaking, the effective potential exhibits infrared (IR) divergences in the limit of vanishing Goldstone masses. By considering the multiplicative anomaly that arises due to non-factorisation of elliptic operators in the Fermi gauge when computing the effective potential at one-loop order, we demonstrate that its gauge independence and IR behaviour are improved to the corresponding findings of Landau gauge calculations simultaneously. The latter are straightforwardly and transparently reproduced using an approach that employs the Heat Kernel technique, thereby providing a shortcut to reflect anomaly-related cancellations from the outset. Our findings generalise to the treatment of the effective potential at finite temperature. In particular, the Heat Kernel extends gauge independence to any value of the expansion in mass over temperature.