Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and 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.

34 pages, 2 figures. Presentation improved and title changed according to referee suggestions. Replaced by revised version, to be published in Phis. Rev. D

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