Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and the transition from integrability to chaos

TL;DR

This paper uncovers a supersymmetric extension of a gauged non-linear sigma model, revealing a transition from integrability to chaos influenced by supersymmetry in a topologically non-trivial sector.

Contribution

It demonstrates the existence of a supersymmetric structure in a gauged non-linear sigma model and explores its impact on the transition from integrability to chaos.

Findings

Existence of a hidden (1+1)-dimensional supersymmetry with N=2 supercharges.

Identification of a topologically non-trivial sector with 'lasagna'-like configurations.

Analysis of how supersymmetry affects the transition from integrability to chaos.

Abstract

The non-linear $\Sigma$-Model minimally coupled with Maxwell theory in $3+1$ dimensions possesses a topologically non-trivial sector characterized by ``lasagna''-like configurations. We demonstrate that, when a specific quantization condition is met, the associated second-order field equations admit a first-order Bogomol'nyi-Prasad-Sommerfield system. This discloses a hidden $(1+1)$-dimensional supersymmetry with $\mathcal{N}=2$ supercharges. We examine the supersymmetric imprint on the time-dependent regime, with particular emphasis on the transition from integrability to chaos.