On the General Structure of the Non-Abelian Born-Infeld Action

TL;DR

This paper explores the structure of the non-abelian Born-Infeld action in flat space, using string theory and non-commutative geometry to derive constraints and explicit solutions, especially in two dimensions.

Contribution

It introduces a method to constrain and explicitly solve the non-abelian Born-Infeld action using invariance under non-commutativity scale changes, including explicit solutions in two dimensions.

Findings

Derived algebraic equations relating terms in the alpha-prime expansion.

Solved these equations explicitly for D=2.

Constructed the minimal invariant derivative extension of the NBI action.

Abstract

We discuss the general structure of the non-abelian Born-Infeld action, together with all of the alpha-prime derivative corrections, in flat D-dimensional space-time. More specifically, we show how the connection between open strings propagating in background magnetic fields and gauge theories on non-commutative spaces can be used to constrain the form of the effective action for the massless modes of open strings at week coupling. In particular, we exploit the invariance in form of the effective action under a change of non-commutativity scale of space-time to derive algebraic equations relating the various terms in the alpha- prime expansion. Moreover, we explicitly solve these equations in the simple case D=2, and we show, in particular, how to construct the minimal invariant derivative extension of the NBI action.