Seiberg-Witten Map for D-branes in Large R-R Field Background

TL;DR

This paper derives a Seiberg-Witten map for D-branes in large R-R field backgrounds, extending to non-Abelian gauge groups, and explores dualities to connect non-commutative and commutative descriptions.

Contribution

It provides a novel Seiberg-Witten map for multiple D-branes in large R-R backgrounds, including non-Abelian extensions and duality analyses.

Findings

Derived the Seiberg-Witten map up to first order in inverse R-R background.

Established a commutative description for non-Abelian D-branes in large R-R fields.

Confirmed the consistency of the map with electromagnetic duality.

Abstract

We obtain a Seiberg-Witten map for the gauge sector of multiple D$p$-branes in a large R-R $(p-1)$-form field background up to the first-order in the inverse R-R field background. By applying the Seiberg-Witten map and then electromagnetic duality on the non-commutative D3-brane theory in the large R-R 2-form background, we find the expected commutative diagram of the Seiberg-Witten map and electromagnetic duality. Extending the U(1) gauge group to the U($N$) gauge group, we obtain a commutative description of the D-branes in the large R-R field background. This construction is different from the known result.