D2-branes in B fields

TL;DR

This paper investigates how D2-branes in type IIA string theory interact with background B fields, showing that D0-brane charge contributions are canceled by bulk effects, clarifying charge quantization issues.

Contribution

It demonstrates the cancellation of D0-brane charge from the B field coupling for compact D2-branes, linking the phenomenon to momentum conservation in M-theory.

Findings

D0-brane charge from B field coupling is canceled by bulk contributions.

The cancellation is explained via momentum conservation in M-theory.

Resolves a recent puzzle on R-R charge quantization on D2-branes in SU(2).

Abstract

This note focuses on the coupling of a type IIA D2-brane to a background B field. It is shown that the D0-brane charge arising from the integral over the D2-brane of the pullback of the B field is cancelled by bulk contributions, for a compact D2-brane wrapping a homotopically trivial cycle in space-time. In M-theory this cancellation is a straightforward consequence of momentum conservation. This result resolves a puzzle recently posed by Bachas, Douglas and Schweigert related to the quantization of R-R charges on stable spherical D2-branes on the group manifold SU(2).