Ramzi R. Khuri

We present a dyonic embedding of the extreme Reissner-Nordstr\"om black hole in $N=4$ and $N=8$ supergravity that breaks all supersymmetries.

We study the embedding of extreme (multi-) dilaton black hole solutions for the values of the parameter $a=\sqrt{3},1,1/\sqrt{3},0$ in $N=4$ and $N=8$ four-dimensional supergravity. For each black hole solution we find different embeddings in $N=4$ supergravity which have different numbers of unbroken supersymmetries. When embedded in $N=8$ supergravity, all different embeddings of the same solution have the same number of unbroken supersymmetries. Thus, there is a relation between the value of the parameter $a$ and the number of unbroken supersymmetries in $N=8$ supergravity, but not in $N=4$, and the different embeddings must be related by dualities of the $N=8$ theory which are not dualities of the $N=4$ theory. The only exception in this scheme is a {\it dyonic} embedding of the $a=0$ black-hole solution which seems to break all supersymmetries both in the $N=4$ and in the $N=8$ theories.

In a recent paper, Duff and Rahmfeld argued that certain massive ${\mathit{N}}_{\mathit{R}}$=1/2 states of the four-dimensional heterotic string correspond to extreme black hole solutions. We provide further, dynamical, evidence for this identification by comparing the scattering of these elementary string states with that of the corresponding extreme black holes, in the limit of low velocities. © 1995 The American Physical Society.

We derive double dimensional reduction/oxidation in a framework where it is applicable to describe general non-static (and anisotropic) $p$-brane solutions. Given this procedure, we are able to relate the dynamical interaction potential for parallel extremal $p$-branes in $D$ dimensions to that for extremal black holes in $D-p$ dimensions. In particular, we find that to leading order the potential vanishes for all $\kappa$-symmetric $p$-branes.