Conical Defects, Black Holes and Higher Spin (Super-)Symmetry

TL;DR

This paper explores the symmetries of classical solutions in higher spin (super-)gravity in AdS3, identifying smooth conical defects and analyzing the supersymmetry properties of higher spin black holes.

Contribution

It classifies all smooth conical defects in various higher spin gravity theories and examines the supersymmetry preservation of higher spin black holes.

Findings

Smooth conical defects correspond to highest weight representations.

Black holes generally break supersymmetry, but some preserve partial supersymmetry.

Holonomy around the spatial circle encodes the symmetries of solutions.

Abstract

We study the (super-)symmetries of classical solutions in the higher spin (super-)gravity in AdS$_3$. We show that the symmetries of the solutions are encoded in the holonomy around the spatial circle. When the spatial holonomies of the solutions are trivial, they preserve maximal symmetries of the theory, and are actually the smooth conical defects. We find all the smooth conical defects in the $sl(N), so(2N+1),sp(2N), so(2N), g_2$, as well as in $sl(N|N-1)$ and $osp(2N+1|2N)$ Chern-Simons gravity theories. In the bosonic higher spin cases, there are one-to-one correspondences between the smooth conical defects and the highest weight representations of Lie group. Furthermore we investigate the higher spin black holes in $osp(3|2)$ and $sl(3|2)$ higher spin (super-)gravity and find that they are only partially symmetric. In general, the black holes break all the supersymmetries, but in some cases they preserve part of the supersymmetries.