Supersymmetric conical defects: Towards a string theoretic description of black hole formation

Abstract

Conical defects, or point particles, in ${\mathrm{AdS}}_{3}$ are one of the simplest nontrivial gravitating systems, and are particularly interesting because black holes can form from their collision. We embed the BPS conical defects of three dimensions into the $\mathcal{N}=4b$ supergravity in six dimensions, which arises from the IIB string theory compactified on K3. The required Kaluza-Klein reduction of the six dimensional theory on a sphere is analyzed in detail, including the relation to the Chern-Simons supergravities in three dimensions. We show that the six dimensional spaces obtained by embedding the 3D conical defects arise in the near-horizon limit of rotating black strings. Various properties of these solutions are analyzed and we propose a representation of our defects in the CFT dual to asymptotically ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{3}$ spaces. Our work is intended as a first step towards analyzing colliding defects that form black holes.