Instanton Corrections to the MSTB Kink Mass

TL;DR

This paper calculates quantum corrections to the mass difference between two degenerate kinks in the MSTB model using instanton techniques, providing an analytic approximation for the splitting.

Contribution

It constructs the instanton connecting the two kinks and derives a simple formula for the mass splitting in the quantum theory.

Findings

Derived an analytic expression for the mass splitting.

Identified the quantum states as symmetric and antisymmetric combinations.

Applied instanton gas approximation to the kink sector.

Abstract

The Montonen-Sarker-Trullinger-Bishop (MSTB) model enjoys two classically degenerate kink solutions in the same topological sector. We construct the instanton that interpolates between them and argue that the two lowest lying Hamiltonian eigenstates in the kink sector of the corresponding quantum theory correspond to symmetric and antisymmetric combinations of coherent states localized at these two solutions. We use the instanton gas approximation to provide a simple, analytic formula for the leading contribution to the mass splitting between these two states.