Symmetry enhancement of Killing horizons in D = 6 supergravity

Abstract

We investigate the near-horizon geometry of supersymmetric extremal black holes in 6-dimensional gauged supergravity. We solve the Killing spinor equations along the lightcone and establish the independent differential and algebraic conditions which are given as the naive restriction of the KSEs on S. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a (super)symmetry enhancement. This follows from generalized Lichnerowicz-type theorems for the zero modes of the Dirac operator and an index theory argument. We also prove that horizons with non-trivial fluxes admit an sl(2, R) symmetry group.