Boundary bound states in the SUSY sine-Gordon model with Dirichlet boundary conditions

TL;DR

This paper investigates the ground state structure of the supersymmetric sine-Gordon model with Dirichlet boundary conditions using lattice regularization, deriving nonlinear integral equations and identifying different ground state configurations.

Contribution

It introduces a novel analysis of the SUSY sine-Gordon model's ground states via nonlinear integral equations for various boundary parameters.

Findings

Three forms of nonlinear integral equations depending on boundary parameters

Identification of four different ground state pictures through numerical analysis

Proposal of two distinct, non-mixing classes in the SUSY sine-Gordon model

Abstract

We analyze the ground state structure of the supersymmetric sine-Gordon model via the lattice regularization. The nonlinear integral equations are derived for any values of the boundary parameters by the analytic continuation and showed three different forms depending on the boundary parameters. We discuss the state that each set of the nonlinear integral equations characterizes in the absence of source terms. Four different pictures of the ground state are found by numerically studying the positions of zeros in the auxiliary functions. We suggest the existence of two classes in the SUSY sine-Gordon model, which cannot be mixed each other.