D-branes in the WZW model

TL;DR

This paper revises the understanding of D-branes in the WZW model, showing they are confined to integer conjugacy classes rather than filling the entire group, with specific results for the SU(2) case.

Contribution

It demonstrates that D-branes in the WZW model are bound to integer conjugacy classes, providing a new perspective contrary to previous claims.

Findings

D-branes are confined to integer conjugacy classes

In SU(2) level k, there are k-1 two-dimensional D-branes

Two D particles are located at points e and -e

Abstract

It is stated in the literature that D-branes in the WZW-model associated with the gluing condition J = - \bar{J} along the boundary correspond to branes filling out the whole group volume. We show instead that the end-points of open strings are rather bound to stay on `integer' conjugacy classes. In the case of SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and two D particles sitting at the points e and -e.