Type-II defects in the super-Liouville theory

A R Aguirre

doi:10.1088/1742-6596/474/1/012001

Abstract

The introduction of type-II defects is discussed under the Lagrangian formalism and Lax representation for the N = 1 super-Liouville model. We derive a new kind of super-Bäcklund transformation for the model and show explicitly the conservation of the modified energy and momentum, as well as supercharge.

Highlights

The study of two-dimensional integrable field theories in the presence of defects or impurities has evolved into a rich subject in recent years from both classical and quantum points of view [1]-[14]
A generalization of the original Lagrangian description was proposed in [6], by allowing additional degrees of freedom associated with the defect itself, which is called typeII defects
Super-Liouville theory with defects we propose a supersymmetric extension of the type-II defect Lagrangian density described in (1)–(3) for the N = 1 supersymmetric Liouville field theory

Summary

Introduction

The study of two-dimensional integrable field theories in the presence of defects or impurities has evolved into a rich subject in recent years from both classical and quantum points of view [1]-[14]. Several types of bosonic field theories [3, 4] allow this kind of defects preserving modified charges after including some defect contributions Their integrability can be ensured by using the wellknown inverse scattering method formalism where the defect conditions corresponding to frozen Backlund transformations turn to be encoded in the defect matrix [5]. A generalization of the original Lagrangian description was proposed in [6], by allowing additional degrees of freedom associated with the defect itself, which is called typeII defects This alternative framework was analyzed in the cases of the sine/sinh-Gordon, massive free field, Liouville and Tzitzeica-Bullough-Dodd models in [6, 7]. Type-II defect Liouville field theory we will review the type-II defects in the Liouville field theory by using the Lagrangian framework, and present the Lax formalism

Lagrangian description

Defect matrix Let us define the following auxiliary linear system: