Abstract
The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.
Highlights
The presence of integrable defects in the N = 1 supersymmetric sinh-Gordon model was discussed in [14], under the Lagrangian formalism and Backlund transformations
The authors have introduced a “partially” type-II defect in the model since only a fermionic auxiliary field appears in the defect Lagrangian, and the integrability was considered in terms of zero curvature representation
The purpose of this paper is to study the integrability of the N = 1 supersymmetric sinh-Gordon (sshG) model from the defect matrix approach, in order to establish the existence of a generating function for an infinite set of modified conserved quantities
Summary
The Lagrangian density describing the N = 1 sshG model with type-I defects can be written as follows [14],. ∂x2φp − ∂t2φp = 8 sinh(2φp) + 8 ψpψp sinh φp, (∂x − ∂t)ψp = 4 ψp cosh φp, (∂x + ∂t)ψp = 4 ψp cosh φp, p = 1, 2,. The eqns (2.8)–(2.13) become the Backlund transformations for the supersymmetric sinhGordon model [16]. From this Lagrangian density we derive the canonical momentum. After introducing the defect at x = 0, the corresponding supercharges read as follows,. 2ψ1 ∂+φ1 − 4ψ1 sinh φ1 − 2ψ2 ∂+φ2 + 4ψ2 sinh φ2. By considering the defect conditions (2.8)–(2.12), we find that the modified conserved supercharges take the following form [17],
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