Fermions in a Reissner-Nordstr\"{o}m-anti-de Sitter Black Hole Background and $N=4$ Supersymmetry with non-trivial Topological Charges

Abstract

We demonstrate that the fermions in Reissner-Nordstr\"{o}m-anti-de Sitter black hole background in the chiral limit $m=0$, are related to an $N=4$ extended one dimensional supersymmetry with non-trivial 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 possess, to have a trivial central charge. The implications of the trivial central charge on the Witten index are also discussed.