Banados and SUSY: On Supersymmetry and Minimal Surfaces of Locally AdS3 Geometries

TL;DR

This paper classifies supersymmetric geometries in locally AdS3 beyond BTZ black holes, linking supersymmetries to solutions of the Hill equation, and uses this to identify extremal surfaces relevant for holographic entanglement entropy.

Contribution

It extends the classification of supersymmetric AdS3 geometries to Banados geometries and introduces a novel method to find extremal surfaces using supersymmetry.

Findings

Supersymmetries correspond to solutions of the Hill differential condition.

Number of global supersymmetries is an orbit invariant.

Supersymmetry helps identify extremal surfaces for holographic entanglement entropy.

Abstract

We extend the classification of supersymmetric locally AdS$_3$ geometries, beyond BTZ black holes, to the Banados geometries, noting that supersymmetries are in one-to-one correspondence with solutions to the Hill differential condition. We show that the number of global supersymmetries is an orbit invariant quantity and identify geometries with zero, one, two, three and four global supersymmetries. As an application of our classification, we exploit supersymmetry, which is preserved locally in the bulk, to determine space-like co-dimension two surfaces in AdS$_3$. In the process, we by-pass geodesics or mappings of AdS$_3$, neither of which have an analogue in higher dimensions, to recover known Hubeny-Rangamani-Takayanagi surfaces. Our findings suggest supersymmetry can be exploited to find extremal surfaces in holographic entanglement entropy.