Gravitational domain walls and p-brane distributions

We review the main algebraic aspects that characterize and determine the do main wall solutions of maximal gauged supergravity in various spacetime dim ensions by considering consistent truncations that retain a number of compo nents in the diagonal of the coset space scalar manifold of the theory. Sta rting from the algebraic classification of domain walls in D =4 gauged supe rgravity, we also derive the corresponding solutions in D = 5 and D = 7 dim ensions. From a higher dimensional point of view, these solutions describe the gravitatonal field, in the field theory limit, of a large number of M2- , D3-and M5-branes that are distributed on hypersurfaces in the transverse space to the branes. As a new result we employ a smearing procedure as well as various dualities to list the irreducible curves and the symmetry group s of p-brane distributions for all values of p that are of interest in curr ent applications of string theory. Some emphasis is placed on the presentat ion of new results in the case of NS5-branes.