Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson Lines

TL;DR

This paper formulates a non-commutative gauge invariant action for D-branes under the Seiberg-Witten map, incorporating Wilson lines and T-duality, and verifies its consistency with known super Yang-Mills results in the Seiberg-Witten limit.

Contribution

It presents a manifestly gauge invariant non-commutative D-brane action with Wilson lines, extending it via T-duality and analyzing its physical couplings.

Findings

The action includes non-constant closed string fields and higher derivatives.

Linear couplings reduce to known super Yang-Mills results in the Seiberg-Witten limit.

The proposed action captures all derivative corrections in the Seiberg-Witten limit.

Abstract

We write the recently conjectured action for transformation of the ordinary Born-Infeld action under the Seiberg-Witten map with one open Wilson contour in a manifestly non-commutative gauge invariant form. This action contains the non-constant closed string fields, higher order derivatives of the non-commutative gauge fields through the $*_N$-product, and a Wilson operator. We extend this non-commutative $D_9$-brane action to the action for $D_p$-brane by transforming it under T-duality. Using this non-commutative $D_p$-brane action we then evaluate the linear couplings of the graviton and dilaton to the brane for arbitrary non-commutative parameters. By taking the Seiberg-Witten limit we show that they reduce exactly to the known results of the energy-momentum tensor of the non-commutative super Yang-Mills theory. We take this as an evidence that the non-commutative action in the Seiberg-Witten limit includes properly all derivative correction terms.