Non-commutative world-volume interactions on D-brane and Dirac-Born-Infeld action

TL;DR

This paper derives a non-commutative version of the Dirac-Born-Infeld action for D-branes by solving the Seiberg-Witten differential equation and confirms its consistency with string scattering amplitudes.

Contribution

It provides an explicit solution to the Seiberg-Witten differential equation and expresses the abelian Dirac-Born-Infeld action in terms of non-commutative gauge fields, linking string theory and non-commutative gauge theory.

Findings

Agreement between non-commutative field theory and string scattering amplitudes

Explicit expression for non-commutative gauge fields in terms of ordinary fields

Perturbative string theory encodes solutions to the Seiberg-Witten equation

Abstract

By integrating the Seiberg-Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterparts up to three non-commutative gauge fields. We then use this change of variables to write ordinary abelian Dirac-Born-Infeld action in terms of non-commutative fields. The resulting action is then compared with various low energy contact terms of world-sheet perturbative string scattering amplitudes from non-commutative D$p$-brane. We find completely agreement between the field theory and string theory results. Hence, it shows that perturbative string theory knows the solution of the Seiberg-Witten differential equation.