Fermions in a Reissner-Nordström-anti-de Sitter Black Hole Background and $N=4$ Supersymmetry with non-trivial 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 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.

Substantial changes, presentation changed, reference list updated, similar to journal version. arXiv admin note: text overlap with arXiv:1208.0740