Supergeometry of Three Dimensional Black Holes

TL;DR

This paper explores the algebraic structure of three-dimensional black holes with supersymmetry, constructing solutions as quotients of a supergroup and analyzing their symmetries, including the limit where the cosmological constant vanishes.

Contribution

It introduces an algebraic method to derive supersymmetric properties of 3D black holes using supergroup quotients, connecting geometric and algebraic perspectives.

Findings

Supersymmetries are obtained algebraically from the supergroup structure.

Black hole solutions are constructed as quotients of OSp(1|2;R).

In the zero cosmological constant limit, the vacuum becomes a null orbifold.

Abstract

We show how the supersymmetric properties of three dimensional black holes can be obtained algebraically. The black hole solutions are constructed as quotients of the supergroup $OSp(1|\,2;R)$ by a discrete subgroup of its isometry supergroup. The generators of the action of the isometry supergroup which commute with these identifications are found. These yield the supersymmetries for the black hole as found in recent studies as well as the usual geometric isometries. It is also shown that in the limit of vanishing cosmological constant, the black hole vacuum becomes a null orbifold, a solution previously discussed in the context of string theory.