Integrable Lattice Realizations of N=1 Superconformal Boundary Conditions

TL;DR

This paper constructs integrable boundary conditions for certain superconformal models, including those that preserve superconformal symmetry, and derives formulas for their partition functions and characters.

Contribution

It introduces new integrable boundary conditions that maintain superconformal symmetry and provides explicit formulas for partition functions and superconformal characters.

Findings

Boundary conditions that break superconformal symmetry

Boundary conditions that preserve superconformal symmetry

Derivation of superconformal Verlinde formula

Abstract

We construct integrable boundary conditions for sl(2) coset models with central charges c=3/2-12/(m(m+2)) and m=3,4,... The associated cylinder partition functions are generating functions for the branching functions but these boundary conditions manifestly break the superconformal symmetry. We show that there are additional integrable boundary conditions, satisfying the boundary Yang-Baxter equation, which respect the superconformal symmetry and lead to generating functions for the superconformal characters in both Ramond and Neveu-Schwarz sectors. We also present general formulas for the cylinder partition functions. This involves an alternative derivation of the superconformal Verlinde formula recently proposed by Nepomechie.