Symmetry of Bounce Solutions at Finite Temperature

TL;DR

This paper extends the symmetry analysis of bounce solutions from zero to finite temperature, proving that the least-action configurations are symmetric and monotonic, thus supporting assumptions used in thermal decay and cosmology.

Contribution

It rigorously proves that at finite temperature, the least-action bounce solutions are $O(D-1)$-symmetric and monotonic, generalizing zero-temperature results.

Findings

Least-action solutions are $O(D-1)$-symmetric at finite temperature

Solutions are monotonic in spatial directions

Provides mathematical justification for symmetry assumptions in thermal decay studies

Abstract

The seminal work of Coleman, Glaser, and Martin established that, at zero temperature, any non-trivial solution to the equations of motion with the least Euclidean action is $O(D)$-symmetric. This paper extends their foundational analysis to finite temperature. We rigorously prove that for a broad class of scalar potentials, any saddle-point configuration with the least action is necessarily $O(D\!-\!1)$-symmetric and monotonic in the spatial directions. This result provides a firm mathematical justification for the symmetry properties widely assumed in studies of thermal vacuum decay and cosmological phase transitions.