Semi-BPS sphaleron and its dynamics

TL;DR

This paper constructs a field theory model featuring a semi-BPS sphaleron bound to an impurity, exploring its unique static properties and dynamic decay behavior, akin to BPS solitons but with inherent instability.

Contribution

It introduces a novel semi-BPS sphaleron-impurity system with no static force, and analyzes its dynamic decay processes, expanding understanding of unstable saddle-point solutions.

Findings

No static force between sphaleron and impurity

Sphaleron exhibits decay dynamics despite BPS-like properties

System bridges BPS solitons and unstable saddle points

Abstract

We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore such a sphaleron-impurity system is very much like usual BPS multi-solitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.