D-branes in Lie groups of rank > 1

TL;DR

This paper analyzes the stability and symmetry-breaking of D-branes in higher-rank Lie groups using an effective action approach, extending known results from SU(2) to more complex groups.

Contribution

It provides a stability analysis of D-branes in higher-rank Lie groups and suggests the universality of the fuzzy sphere configuration as the ground state.

Findings

Effective action is bounded from below.

Higher-rank Lie groups exhibit symmetry-breaking in D-brane ground states.

Fuzzy sphere D2-brane may be the stable configuration beyond SU(2).

Abstract

We consider a low-energy effective action for the gauge field on Wess-Zumino-Witten D-branes in a compact simple Lie group, in the limit of large k. We prove that the effective action is bounded from below, and study stability of various D-brane configurations, including some class of non-maximally symmetric ones. We show that for Lie groups of rank higher than one, the D-brane ground state breaks the Kac-Moody symmetry of the boundary theory. We then give arguments hinting that the "fuzzy sphere" D2-brane which is known to be the stable brane configuration in the case of SU(2), may also correspond to the ground state in other compact simple Lie groups.