Exact One-Loop Thermal Free Energies of Solitons

TL;DR

This paper presents a method to compute the exact one-loop thermal free energy corrections for solitons using scattering theory, applicable to models like $^4$ in various dimensions, enhancing precision in quantum soliton analysis.

Contribution

The paper introduces a novel technique combining the effective potential and scattering theory to accurately calculate one-loop thermal free energies of solitons.

Findings

Exact free energy for kink in 1+1 dimensions computed.

Exact free energy for domain wall in 2+1 dimensions obtained.

Method efficiently integrates quantum and thermal corrections.

Abstract

I show how to compute the exact one-loop thermal correction to the free energy of a soliton. The method uses the effective potential as an auxiliary step to ensure that the soliton is quantized around the appropriate vacuum. The exact result is then computed using scattering theory techniques, and includes all orders in the derivative expansion. It can be efficiently combined with a calculation of the exact quantum correction to yield the full free energy to one loop. I demonstrate this technique with explicit computations in $\phi^4$ models, obtaining the free energy for a kink in 1+1 dimensions and a domain wall in 2+1 dimensions.