Existence of a supersymmetric extension of the gauged nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math> model and the transition from integrability to chaos

The nonlinear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Σ</a:mi></a:math> model minimally coupled with Maxwell theory in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mn>3</d:mn><d:mo>+</d:mo><d:mn>1</d:mn></d:math> dimensions possesses a topologically nontrivial sector characterized by 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 the existence of a (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mn>1</f:mn><f:mo>+</f:mo><f:mn>1</f:mn></f:mrow></f:math>)-dimensional supersymmetric extension with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="script">N</h:mi><h:mo>=</h:mo><h:mn>2</h:mn></h:math> supercharges. We examine its imprint on the time-dependent regime, with particular emphasis on the transition from integrability to chaos.