Distributed systems of intersecting branes at arbitrary angles

A 'reduced' action formulation for a general class of the supergravity solu tions, corresponding to the 'marginally' bound 'distributed' systems of var ious types of branes at arbitrary angles, is developed. It turns out that a ll the information regarding the classical features of such solutions is en coded 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-dimension al submanifold of the fields' configuration (target) space, parametrized by a set of N independent harmonic functions on the transverse space. This su bmanifold, 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 Lagra ngian. The equations of motion then transform to a set of equations describ ing the embedding of a null geodesic surface in this space, which is identi fied as the H-surface. Using these facts, we present a very simple derivati on of the conventional orthogonal solutions together with their intersectio n rules. Then a new solution for a (distributed) pair of p-branes at SU(2) angles in D dimensions is derived. (C) 1999 Published by Elsevier Science B .V.