RR charges of D2-branes in the WZW model

TL;DR

This paper investigates how the B-field affects the RR charge of spherical D2-branes in the SU(2) WZW model, revealing that charges are only well-defined modulo a certain level-dependent integer.

Contribution

It extends previous analyses by showing boundary and bulk contributions to RR charge do not cancel and provides a formula for RR charges in the SU(2) WZW model at level k.

Findings

RR charges are only defined modulo k+2

Boundary and bulk contributions add up to an integer

Supports findings with D0-brane bound state analysis

Abstract

We consider the contribution of the B-field into the RR charge of a spherical D2-brane. Extending a recent analysis of Taylor, we show that the boundary and bulk contributions do not cancel in general. Instead, they add up to an integer as observed by Stanciu. The general formula is applied to compute the RR charges of spherical D-branes of the SU(2) WZW model at level k and it shows that these RR charges are only defined modulo k+2. We support this claim by studying bound state formation of D0-branes using boundary conformal field theory.