We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous fiveform flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.

We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, F 10 , and to those of the 'massive' IIA theory for non-vanishing F 10 . We present a multi 8-brane solution of these equations that generalizes the 8-brane of Polchinski and Witten. We show that this solution is T-dual to a new multi 7-brane solution of S 1 compactified IIB supergravity, and that the latter is T-dual to the IIA 6-brane. When combined with the Sl(2; Z) U-duality of the type IIB superstring, the T-duality between type II 7-branes and 8-branes implies a quantization of the cosmological constant of type IIA superstring theory. These results are made possible by the construction of a new massive N=2 D=9 supergravity theory. We also discuss the 11-dimensional interpretation of these type II p-branes.2

We show that the maximally supersymmetric pp-wave of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS ×S solutions. In addition we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS ×S background is either Minkowski space or a maximally supersymmetric pp-wave.

Abstract. We investigate the Penrose limits of classical string and Mtheory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS ×S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born-Infeld type.

We present the magnetic duals of Güven's electric-type solutions of D=11 supergravity preserving 1/4 or 1/8 of the D=11 supersymmetry. We interpret the electric solutions as n orthogonal intersecting membranes and the magnetic solutions as n orthogonal intersecting 5-branes, with n = 2, 3; these cases obey the general rule that p-branes can self-intersect on (p − 2)-branes. On reduction to D = 4 these solutions become electric or magnetic dilaton black holes with dilaton coupling constant a = 1 (for n = 2) or a = 1/ √ 3 (for n = 3). We also discuss the reduction to D=10.