Distributed systems of intersecting branes at arbitrary angles

Abstract

A ‘reduced’ action formulation for a general class of the supergravity solutions, corresponding to the ‘marginally’ bound ‘distributed’ systems of various types of branes at arbitrary angles, is developed. It turns out that all the information regarding the classical features of such solutions is encoded in a first-order Lagrangian (the ‘reduced’ Lagrangian) corresponding to the desired geometry of branes. The marginal solution for a system of N such distributions (for various distribution functions) span an N-dimensional submanifold of the fields' configuration (target) space, parametrized by a set of N independent harmonic functions on the transverse space. This submanifold, which we call the ‘ H-surface’, is a null surface with respect to a metric on the configuration space, which is defined by the reduced Lagrangian. The equations of motion then transform to a set of equations describing the embedding of a null geodesic surface in this space, which is identified as the H-surface. Using these facts, we present a very simple derivation of the conventional orthogonal solutions together with their intersection rules. Then a new solution for a (distributed) pair of p-branes at SU(2) angles in D dimensions is derived.