Up to overall harmonic factors, the D8-brane solution of the massive type IIA supergravity theory is the product of nine-dimensional Minkowski space (the worldvolume) with the real line (the transverse space). We show that the equations of motion allow for the worldvolume metric to be generalised to an arbitrary Ricci-flat one. If this nine-dimensional Ricci-flat manifold admits Killing spinors, then the resulting solutions are supersymmetric and satisfy the usual Bogomol'nyi bound, although they preserve fewer than the usual one half of the supersymmetries. We describe the possible choices of such manifolds, elaborating on the connection between the existence of Killing spinors and the self-duality condition on the curvature two-form. Since the D8-brane is a domain wall in ten dimensions, we are led to consider the general case: domain walls in any supergravity theory. Similar considerations hold here also. Moreover, it is shown that the worldvolume of any magnetic brane -of which the domain walls are a specific example -can be generalised in precisely the same way. The general class of supersymmetric solutions have gravitational instantons as their spatial sections. Some mention is made of the worldvolume solitons of such branes. 1

This paper considers the spacetimes describing pp-waves propagating on extremal non-dilatonic branes. It is shown that an observer moving along a geodesic will experience infinite curvature at the horizon of the brane, which should therefore be regarded as singular. Taking the decoupling limit of these brane-wave spacetimes gives a pp-wave in AdS, the simplest example being the Kaigorodov spacetime. It has been conjectured that gravity in this spacetime is dual to a CFT in the infinite momentum frame with constant momentum density. If correct, this implies that the CFT must resolve the singularity of the bulk spacetime. Evidence in favour of this conjecture is presented. The unbroken conformal symmetries determine the scalar 2-point function up to an arbitrary function of one variable. However, an AdS/CFT calculation shows that this function is constant (to leading order in 1/N 2 ) and the result is therefore the same as when the full conformal symmetry is unbroken. This paper also discusses a recently discovered Virasoro symmetry of metrics describing pp-waves in AdS and naked singularities in the Randall-Sundrum scenario. * email: Dominic.Brecher@durham.ac.uk †

We argue that the trace structure of the non-abelian Born-Infeld action can be fixed by demanding that the action be linearised by certain energyminimising BPS-like configurations. It is shown how instantons in D4-branes, SU(2) monopoles and dyons in D3-branes, and vortices in D2-branes are all BPS states of the action recently proposed by Tseytlin. All such configurations can be dealt with exactly within the context of non-abelian Born-Infeld theory since, given the relevant BPS-like condition, the action reduces to that of Yang-Mills theory. It would seem, moreover, that such an analysis holds for the symmetrised trace structure of Tseytlin's proposal only.1 email d.r.brecher@damtp.cam.ac.uk.

We attempt to settle the issue as to what is the correct non-abelian generalisation of the Born-Infeld action, via a consideration of the two-loop β-function for the non-abelian background gauge field in open string theory. An analysis of the bosonic theory alone shows the recent proposal of Tseytlin's [1] to be somewhat lacking. For the superstring, however, this proposal would seem to be correct, and not just within the approximation used in [1]. Since it is this latter case that is relevant to the description of D-branes we, in effect, obtain an independent verification of Tseytlin's result. Some issues involved in the concept of non-abelian T-duality are discussed; and it is shown how the interaction between separated and parallel branes, in the form of massive string states, emerges. 1

Matrix string theory is equivalent to type IIA superstring theory in the light-cone gauge, together with extra degrees of freedom representing D-brane states. It is therefore the appropriate framework in which to study systems of multiple fundamental strings expanding into higher-dimensional D-branes. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. As a check, we show that at weak coupling the resulting action reproduces light-cone gauge string theory in a weakly curved background. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding. We comment on the dielectric effect in each of these theories, giving some explicit solutions describing fundamental strings expanding into various Dp-branes.