Classification and Quantum Moduli Space of D-branes in Group Manifolds

TL;DR

This paper classifies D-branes in all compact Lie groups, analyzes their quantum moduli space, and explores the existence of singular D-branes at the quantum level, providing explicit constructions and topological insights.

Contribution

It offers a comprehensive classification of D-branes in all compact Lie groups, including non-simply-laced cases, and investigates the global structure of their quantum moduli space.

Findings

Explicit classification of D-branes in rank 2 groups

Construction of D-branes in higher-rank groups using Dynkin diagram methods

Identification of singular D-branes at the quantum level

Abstract

We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the maximal torus. We describe rank 2 cases, namely $B_2$, $C_2$, $G_2$, explicitly and construct all the D-branes in $B_r$, $C_r$, $F_4$ by the method of iterative deletion in the Dynkin diagram. The discussion of moduli space involves global issues that can be treated in terms of the exact homotopy sequence and various lattices. We also show that singular D-branes can exist at quantum mechanical level.