Bound States of D-Branes and the Non-Abelian Born-Infeld Action

TL;DR

This paper investigates the correct non-abelian generalization of the Born-Infeld action for D-branes using two-loop beta-function calculations in string theory, providing support for Tseytlin's proposal in the superstring case.

Contribution

It offers an independent verification of Tseytlin's non-abelian Born-Infeld action proposal through two-loop beta-function analysis in superstring theory.

Findings

Tseytlin's proposal is supported for superstring theory.

Analysis of non-abelian T-duality issues is provided.

Interaction between separated branes via massive string states is shown.

Abstract

We attempt to settle the issue as to what is the correct non-abelian generalisation of the Born-Infeld action, via a consideration of the two-loop $\beta$--function for the non-abelian background gauge field in open string theory. An analysis of the bosonic theory alone shows the recent proposal of Tseytlin's to be somewhat lacking. For the superstring, however, this proposal would seem to be correct, and not just within the approximation used in \cite{tseytlin}. Since it is this latter case that is relevant to the description of D-branes we, in effect, obtain an independent verification of Tseytlin's result. Some issues involved in the concept of non-abelian T--duality are discussed; and it is shown how the interaction between separated and parallel branes, in the form of massive string states, emerges.