Relation between Commutative and Non-Commutative Descriptions of D-branes in Large R-R Field Background

TL;DR

This paper derives the Seiberg-Witten map for D-branes in large R-R backgrounds, revealing differences in non-locality between Abelian and non-Abelian sectors and providing insights into brane dynamics.

Contribution

It presents the first-order Seiberg-Witten map for D-branes with large R-R fields, clarifying non-locality sources and linking commutative and non-commutative descriptions.

Findings

In SU(N) sector, the map introduces non-local operators.

In U(1) sector, non-locality can be removed.

Provides insights into Dirac-Born-Infeld and M5-brane dynamics.

Abstract

We derive the Seiberg-Witten map to first order in the non-commutativity parameter for D-branes in the presence of a large R-R background field. This result enables a systematic investigation of the commutative formulation of the corresponding Lagrangian. In the SU($N$) sector, the map introduces a non-local operator. In contrast, in the U(1) sector, this non-locality can be removed. This contrast suggests that the essential source of non-local behavior lies in the non-Abelian degrees of freedom. The commutative description obtained here offers further insight into both the Dirac-Born-Infeld structure and its possible extensions to the dynamics of M5-branes.