Interacting D2-branes in 10 dimensions and non abelian Born-Infeld theory

TL;DR

This paper extends the bosonic D2-brane action to an SU(2) non-abelian system, deriving a non-abelian Born-Infeld theory that aligns with superstring amplitude results, offering a new analytical approach.

Contribution

It introduces a non-abelian SU(2) extension of the D2-brane action with off-shell algebra closure and derives the corresponding Born-Infeld theory.

Findings

The SU(2) D-brane action has only first class constraints.

The algebra of constraints closes off-shell.

The derived non-abelian Born-Infeld theory matches superstring amplitude calculations up to fourth order.

Abstract

In this paper we extend the bosonic $D$-brane action in D=10 obtained by duality from the D=11 membrane wrapped on $S^1$ to an SU(2) non abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the $D2$-brane to include non abelian symmetry generators. From the SU(2) $D$-brane action, we also obtain the SU(2) Born-Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyze non-abelian Born-Infeld theories.