D-branes in group manifolds

TL;DR

This paper explores the geometric interpretation of boundary conditions in WZW models, revealing how they determine D-brane configurations, including twisted conjugacy classes and subgroup/coset structures.

Contribution

It provides a detailed analysis of gluing conditions in WZW models, linking boundary conditions to specific D-brane worldvolume geometries, including affine symmetry-preserving and subgroup-based configurations.

Findings

Boundary conditions encode D-brane geometries in WZW models.

Twisted conjugacy classes describe affine symmetry-preserving D-branes.

Subgroup and coset configurations expand the types of D-branes in these models.

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.