SU(2) WZW D-branes and their non-commutative geometry from DBI action

TL;DR

This paper explores D-branes on a three-sphere in string theory, showing their stability via background fields and linking their dynamics to non-commutative Yang-Mills theory at large sphere radius.

Contribution

It demonstrates how D-branes on $S^3$ are described by conjugacy classes and connects their large-radius behavior to non-commutative gauge theories, extending previous results.

Findings

D-branes correspond to conjugacy classes of SU(2)

Branes are stabilized by NSNS background

Large $Q_5$ limit yields non-commutative Yang-Mills dynamics

Abstract

Using properties of the DBI action we find D-branes on $S^3$ of the radius $Q_5$ corresponding to the conjugacy classes of SU(2). The branes are stable due to nonzero 2-form NSNS background. In the limit of large $Q_5$ the dynamics of branes is governed by the non-commutative Yang-Mills theory. The results partially overlap with those obtained in the recent paper hep-th/0003037.