Supersymmetric Conical Defects: Towards a string theoretic description of black hole formation

TL;DR

This work embeds three-dimensional supersymmetric conical defects into six-dimensional ${ m N}=4b$ supergravity arising from type IIB string theory on ${ m K3}$, using a sphere ${ m S}^{3}$ KK reduction to connect to a 3d ${ m SU}(1,1|2) imes{ m SU}(1,1|2)$ CS supergravity framework. The authors show how to realize BPS conical defects via a fibered ${ m S}^{3}$ over ${ m AdS}_{3}$, with holonomies implemented by KK gauge fields, and they relate these defects to the near-horizon geometries of spinning black strings, including global ${ m AdS}_{3}$ at special parameter values. A dual description in the boundary CFT RR sector is proposed, utilizing spectral flow to map bulk Wilson lines to boundary charges and density matrices, thereby offering a non-perturbative holographic picture of defect states. The results establish a concrete setup to study the collision of defects that form black holes and set the stage for further tests of AdS/CFT in backgrounds with conical defects and reduced supersymmetry.

Abstract

Conical defects, or point particles, in AdS_3 are one of the simplest non-trivial 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 N=4b supergravity in six dimensions, which arises from 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 AdS_3 x S^3 spaces. Our work is intended as a first step towards analyzing colliding defects that form black holes.