Composite BPS configurations of p -branes in 10 and 11 dimensions

Abstract

We give an overview of various composite BPS configurations of string theory and M-theory p-branes represented as classical supergravity solutions. Type II string backgrounds can be obtained by S- and T-dualities from the NS - NS configurations corresponding to exact conformal sigma-models. The single-centre solutions can also be generated from the Schwarzschild solution by applying a sequence of boosts, `smearings' in some number of dimensions, dualities and taking the extremal limit. The basic `marginal' backgrounds representing threshold BPS bound states of branes are parametrized by a number of independent harmonic functions, one for each brane. `Non-marginal' BPS configurations in D = 10 can be constructed from the marginal ones using U-duality and thus are parametrized, in addition to harmonic functions, by a finite number of O(d,d) and SL(2,R) `angles'. Some of them can be viewed as dimensional reductions of coordinate-transformed (boosted or rotated) marginal configurations of M-branes. We present a new more general class of configurations in which some of the branes or their intersection spaces are localized on other branes. In particular, we find the supergravity background describing the type II BPS configuration of a 3-brane, RR 5-brane and NS - NS 5-brane, and a related `localized' 2-5-5 D = 11 solution. We also consider the classical action for a 3-brane probe moving in such type IIB backgrounds and determine the structure of the corresponding moduli space metrics.