Quasi-Integrability in Supersymmetric Sine-Gordon Models

TL;DR

This paper demonstrates that a deformed supersymmetric sine-Gordon model exhibits quasi-integrability with finite conserved quantities, influenced by boundary conditions, and reveals unique algebraic structures not present in non-supersymmetric versions.

Contribution

It introduces the concept of quasi-integrability in supersymmetric sine-Gordon models and highlights the role of boundary conditions and new algebraic structures.

Findings

The model is quasi-integrable with finite conserved charges.

Boundary conditions are crucial for maintaining quasi-integrability.

New algebraic structures emerge in the supersymmetric case.

Abstract

The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly possesses finite number of conserved quantities, leaving-out an infinite number of non-conserved anomalous charges. The quasi-integrability of this supersymmetric model heavily rely on the boundary conditions of the potential, otherwise rendered to be completely non-integrable. Moreover, interesting additional algebraic structures appear, absent in the non-supersymmetric counterparts.