Classical Integrable N=1 and $N= 2$ Super Sinh-Gordon Models with Jump Defects

TL;DR

This paper explores integrable N=1 and N=2 super sinh-Gordon models with jump defects, constructing boundary functions that generate Bäcklund transformations and demonstrating supersymmetry invariance.

Contribution

It introduces explicit boundary functions for super sinh-Gordon models with jump defects, linking them to Bäcklund transformations and providing new solutions involving fermions.

Findings

Boundary functions generate Bäcklund transformations.

Models exhibit supersymmetry invariance.

New solution with incoming boson and outgoing fermion.

Abstract

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N=1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.