The Non-Abelian Born-Infeld Action and Noncommutative gauge theory

TL;DR

This paper demonstrates the equivalence between the non-Abelian Born-Infeld action and noncommutative gauge theory for D-branes, confirming key aspects of string theory dualities and providing explicit forms of derivative corrections.

Contribution

It explicitly proves the equivalence between the non-Abelian Born-Infeld action and noncommutative gauge theory for slowly varying fields, and constructs derivative correction terms.

Findings

Confirmed the equivalence between the two descriptions of D-branes.

Derived general forms of 2n-derivative terms for non-Abelian gauge fields.

Validated the Seiberg-Witten conjecture in the context of slowly varying fields.

Abstract

In this paper we explicitly show the equivalence between the non-Abelian Born-Infeld action, which was proposed by Tseytlin as an effective action on several D-branes, and its noncommutative counterpart for slowly varying fields. This confirms the equivalence between the two descriptions of the D-branes using an ordinary gauge theory with a constant B field background and a noncommutative gauge theory, claimed by Seiberg and Witten. We also construct the general forms of the 2 n-derivative terms for non-Abelian gauge fields which are consistent with the equivalence in the approximation of neglecting (2 n+2)-derivative terms.