Fermions in a Reissner–Nordström–anti-de Sitter black hole background and N = 4 supersymmetry with nontrivial topological charges

Abstract

We demonstrate that the fermions in Reissner–Nordström–anti-de Sitter black hole background in the chiral limit m = 0, are related to an N = 4 extended one-dimensional supersymmetry with nontrivial topological charges. We also show that the N = 4 extended supersymmetry is unbroken and we extend the two N = 2 one-dimensional supersymmetries that the system also possesses, to have a trivial central charge. The implications of the trivial central charge on the Witten index are also discussed.