Tricritical Ising Model with a Boundary

TL;DR

This paper investigates the integrable boundary conditions of the supersymmetric tricritical Ising model, deriving exact boundary S-matrices and exploring their relation to boundary conformal field theory perturbations.

Contribution

It provides the first exact boundary S-matrices for the supersymmetric tricritical Ising model with boundary, incorporating topological charge dependence and supersymmetry constraints.

Findings

Derived exact boundary S-matrices depending on topological charge.

Solved the boundary Yang-Baxter equation for this model.

Connected reflection matrices to boundary perturbations in conformal field theory.

Abstract

We study the integrable and supersymmetric massive $\hat\phi_{(1,3)}$ deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary $S$-matrices, which turn out to depend explicitly on the topological charge of the supersymmetry algebra. We also solve the general boundary Yang-Baxter equation and show that in appropriate limits the general reflection matrices go over the supersymmetry preserving solutions. Finally, we briefly discuss the possible connection between our reflection matrices and boundary perturbations within the framework of perturbed boundary conformal field theory.