On the Equivalence between Noncommutative and Ordinary Gauge Theories

TL;DR

This paper demonstrates the equivalence between noncommutative and ordinary gauge theories beyond the Dirac-Born-Infeld approximation by explicitly constructing derivative terms and confirming consistency with superstring theory calculations.

Contribution

It extends the Seiberg-Witten equivalence to include general 2n-derivative terms and verifies the consistency with superstring D-brane actions.

Findings

Explicit forms of 2n-derivative terms satisfying the equivalence.

Proof of consistency with superstring D-brane actions when neglecting higher derivatives.

Extension of the equivalence beyond the Dirac-Born-Infeld approximation.

Abstract

Recently Seiberg and Witten have proposed that noncommutative gauge theories realized as effective theories on D-brane are equivalent to some ordinary gauge theories. This proposal has been proved, however, only for the Dirac-Born-Infeld action in the approximation of neglecting all derivative terms. In this paper we explicitly construct general forms of the 2n-derivative terms which satisfy this equivalence under their assumption in the approximation of neglecting (2 n+2)-derivative terms. We also prove that the D-brane action computed in the superstring theory is consistent with the equivalence neglecting the fourth and higher order derivative terms.