Symmetry enhancement of extremal horizons in D=5 supergravity

TL;DR

This paper proves that near-horizon geometries of supersymmetric extremal black holes in 5D supergravity exhibit supersymmetry enhancement and always admit an sl(2,\u211dR) symmetry group, using Lichnerowicz-type theorems and index theory.

Contribution

It establishes the supersymmetry enhancement and sl(2,R) symmetry for near-horizon geometries in 5D supergravity through new mathematical theorems.

Findings

Near-horizon geometries always admit sl(2,R) symmetry.

Supersymmetry is enhanced in these geometries.

The results apply to both ungauged and gauged supergravity.

Abstract

We consider the near-horizon geometry of supersymmetric extremal black holes in un-gauaged and gauged 5-dimensional supergravity, coupled to abelian vector multiplets. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a supersymmetry enhancement. This follows from a set of generalized Lichnerowicz-type theorems we establish, together with an index theory argument. As a consequence, these solutions always admit a $\mathfrak{sl}(2,\mathbb{R})$ symmetry group.