SU(2) WZW D-branes and quantized worldvolume U(1) flux on S^2

TL;DR

This paper investigates D-brane configurations on SU(2) group manifolds, revealing how boundary conditions affect symmetries and deriving quantized U(1) flux on spherical D2-branes.

Contribution

It demonstrates the relationship between sigma model boundary conditions, symmetry breaking, and flux quantization for D-branes on SU(2) manifolds.

Findings

Chiral Kac-Moody symmetry is broken for most D-branes except spherical D2-branes.

The U(1) flux on spherical D2-branes is quantized and consistent with flux quantization.

Boundary conditions influence the symmetry properties of D-branes in SU(2) models.

Abstract

We discuss possible D-brane configurations on SU(2) group manifolds in the sigma model approach. When we turn the boundary conditions of the spacetime fields into the boundary gluing conditions of chiral currents, we find that for all D-branes except the spherical D2-branes, the gluing matrices R^a_{b} depend on the fields, so the chiral Kac-Moody symmetry is broken, but conformal symmetry is maintained. Matching the spherical D2-branes derived from the sigma model with those from the boundary state approach we obtain a U(1) field strength that is consistent with flux quantization.