Interacting D2 branes in ten dimensions and non-Abelian Born–Infeld theory

Abstract

In this paper we extend the bosonic D-brane action in D = 10 obtained by duality from the D = 11 membrane wrapped on S1 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 analyse non-Abelian Born–Infeld theories.