Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography

TL;DR

This paper explores supersymmetric theories on three-dimensional Lorentzian manifolds with applications to black hole holography, identifying conditions for preserved supersymmetry and relating boundary spinors to bulk black hole solutions.

Contribution

It characterizes the existence of conformal Killing spinors on Lorentzian manifolds and connects these to supersymmetric AdS black hole solutions, providing a boundary perspective on bulk properties.

Findings

Supersymmetry exists when a null or timelike conformal Killing vector is present.

Reproduces the classification of BPS black holes based on magnetic charge from the boundary viewpoint.

Proposes a dual superconformal quantum mechanics on black hole horizons.

Abstract

We study N <= 2 superconformal and supersymmetric theories on Lorentzian threemanifolds with a view toward holographic applications, in particular to BPS black hole solutions. As in the Euclidean case, preserved supersymmetry for asymptotically locally AdS solutions implies the existence of a (charged) "conformal Killing spinor" on the boundary. We find that such spinors exist whenever there is a conformal Killing vector which is null or timelike. We match these results with expectations from supersymmetric four-dimensional asymptotically AdS black holes. In particular, BPS bulk solutions in global AdS are known to fall in two classes, depending on their graviphoton magnetic charge, and we reproduce this dichotomy from the boundary perspective. We finish by sketching a proposal to find the dual superconformal quantum mechanics on the horizon of the magnetic black holes.