Non-maximally symmetric D-branes on group manifold in the Lagrangian approach

TL;DR

This paper provides a group-element based description of non-maximally symmetric D-branes on group manifolds, elucidating T-duality effects and explicitly analyzing SU(2) and SL(2,R) cases.

Contribution

It offers a simple, group-element based framework for describing non-maximally symmetric D-branes, clarifying T-duality effects on conjugacy classes.

Findings

T-duality corresponds to conjugacy class multiplication by U(1) subgroups

Explicit two-form trivializing the WZW three-form is derived

Detailed analysis of SU(2) and SL(2,R) examples

Abstract

Recently, Maldacena, Moore and Seiberg introduced non-maximally symmetric boundary states on group manifold using T-duality. In the work presented here we suggest simple description of these branes in terms of group elements. We show that T-dualization actually reduces to multiplication of conjugacy classes by the corresponding U(1) subgroups. Using this description we find the two-form trivializing the WZW three-form on the branes. SU(2) and $SL(2,R)$ examples are considered in details.