D-Branes on a gauged WZW model

TL;DR

This paper geometrically classifies boundary states (branes) in gauged WZW models, showing they correspond to specific orbits of conjugacy classes on the coset manifold, linking algebraic and geometric perspectives.

Contribution

It provides a geometric realization of the algebraic classification of boundary states in gauged WZW models, connecting conjugacy class orbits to brane configurations.

Findings

Boundary states correspond to H orbits of quantized G conjugacy classes

Branes are shifted by quantized H conjugacy classes

Geometric realization links algebraic and geometric classifications

Abstract

The algebraic classification of Cardy for boundary states on a $G/H$ coset CFT of a compact group G, is geometrically realized on the corresponding manifold resulting from gauging the WZW model. The branes consist of H orbits of quantized G conjugacy classes shifted by quantized H conjugacy classes.