Consistent superconformal boundary states

TL;DR

This paper extends Cardy's boundary state framework to N=1 superconformal models, solving for minimal models and classifying boundary conditions, including novel NS~ states and their symmetries.

Contribution

It introduces a supersymmetric generalization of Cardy's equation and classifies superconformal boundary states for minimal models, including NS, R, and NS~ states.

Findings

Solved superconformal boundary states for SM(p/p+2) models with p odd.

Identified NS, R, and NS~ boundary states and their relations.

Applied the framework to the tricritical Ising model.

Abstract

We propose a supersymmetric generalization of Cardy's equation for consistent N=1 superconformal boundary states. We solve this equation for the superconformal minimal models SM(p/p+2) with p odd, and thereby provide a classification of the possible superconformal boundary conditions. In addition to the Neveu-Schwarz (NS) and Ramond (R) boundary states, there are NS~ states. The NS and NS~ boundary states are related by a Z_2 "spin-reversal" transformation. We treat the tricritical Ising model as an example, and in an appendix we discuss the (non-superconformal) case of the Ising model.