N=1 Worldsheet Boundary Couplings and Covariance of non-Abelian Worldvolume Theory

Abstract

A systematic construction is given for N=1 open string boundary coupling to Abelian and non-Abelian Dp-brane worldvolume fields, in general curved backgrounds. The basic ingredient is a set of four ``boundary vectors'' that provide a unified description of boundary conditions and boundary couplings. We then turn to the problem of apparent inconsistency of non-Abelian worldvolume scalar couplings (obtained by T-duality), with general covariance. It means that the couplings cannot be obtained from a covariant action by gauge fixing ordinary general coordinate transformations (GCT). It is shown that the corresponding worldsheet theory has the same problem, but is also invariant under certain matrix-valued coordinate transformations (MCT) that can be used to restore its covariance. The same transformations act on the worldvolume, leading to a covariant action. Then the non-Abelian Dp-brane action obtained by T-duality corresponds to gauge fixing the MCT and not GCT, hence the apparent incompatibility with general covariance.