Banados and SUSY: On supersymmetry and minimal surfaces of locally AdS₃ geometries

We extend the classification of supersymmetric locally AdS₃ geometries, beyond BTZ black holes, to the Baados 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 AdS₃. In the process, we by-pass geodesics or mappings of AdS₃, neither of which have an analogue in higher dimensions, to recover known Hubeny-Rangamani-Takayanagi surfaces. Our findings suggest supersymmetry may be exploited to find extremal surfaces in holographic entanglement entropy.