D-branes in group manifolds

TL;DR

The paper clarifies how algebraic gluing conditions for chiral currents in WZW models translate into geometric D-brane configurations on group manifolds. It identifies two principal classes: Type-D, preserving affine symmetry and giving D-branes on twisted conjugacy classes, and Type-N, which do not preserve the current algebra and can produce subgroups, cosets, or open submanifolds. The analysis shows that boundary conditions are inherently point-dependent in curved spaces and provides explicit geometric realizations, especially for SU(2). This work helps reconcile boundary-state data with target-space geometry and sets the stage for further exploration of field-dependent gluing and dualities.

Abstract

In this paper we re-examine the geometric interpretation of gluing conditions in WZW models and the possible D-brane configurations that they give rise to. We show how the boundary conditions are encoded in the gluing conditions imposed on the chiral currents. We analyse two special classes of gluing conditions: the first, which preserves the affine symmetry of the bulk theory, describes D-branes whose worldvolumes are given by `twisted' conjugacy classes; the second class describes configurations which include subgroups and cosets.