Superconformal boundary conditions for the WZW model

TL;DR

This paper reviews superconformal boundary conditions for N=1 and N=2 supersymmetric WZW models, revealing a generalized gluing map for affine currents beyond known automorphisms.

Contribution

It introduces a new form of the gluing map for affine currents in superconformal boundary conditions, extending previous automorphism-based approaches.

Findings

Generalized gluing map for affine currents in superconformal boundary conditions

Analysis of boundary conditions for N=1 and N=2 supersymmetric WZW models

Extension of known automorphisms to more general boundary conditions

Abstract

We review the most general, local, superconformal boundary conditions for the two-dimensional N=1 and N=2 non-linear sigma models, and analyse them for the N=1 and N=2 supersymmetric WZW models. We find that the gluing map between the left and right affine currents is generalised in a very specific way as compared to the constant Lie algebra automorphisms that are known.