Index Theory and Supersymmetry of 5D Horizons

Abstract

We prove that the near-horizon geometries of minimal gauged five-dimensional supergravity preserve at least half of the supersymmetry. If the near-horizon geometries preserve a larger fraction, then they are locally isometric to $Ad{S}_5$. Our proof is based on Lichnerowicz type theorems for two horizon Dirac operators constructed from the supercovariant connection restricted to the horizon sections, and on an application of the index theorem. An application is that all half-supersymmetric five-dimensional horizons admit an $\mathfrak{sl}(2,\mathbb{R})$ symmetry subalgebra.

Section 7, on the sl(2,R) symmetry, has been added. 23 pages, latex, uses jheppub.sty

References in corpus (8)

• Near-horizon symmetries of extremal black holes
• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• Classification of Static Charged Black Holes in Higher Dimensions
• Index theory and dynamical symmetry enhancement of M-horizons
• The return of the four- and five-dimensional preons
• Vanishing Preons in the Fifth Dimension
• M-Horizons
• Topology of supersymmetric N=1, D=4 supergravity horizons

Cited by in corpus (15)

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• Supersymmetry of AdS and flat IIB backgrounds
• Index theory and dynamical symmetry enhancement near IIB horizons
• Einstein--Weyl Spaces and Near-Horizon Geometry
• Dynamical symmetry enhancement near IIA horizons
• Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces
• Dynamical symmetry enhancement near massive IIA horizons
• Moduli Spaces of Transverse Deformations of Near-Horizon Geometries
• Dynamical symmetry enhancement near N=2, D=4 gauged supergravity horizons
• Symmetry enhancement of extremal horizons in D=5 supergravity
• Black holes in Sol minore
• Supersymmetric AdS Black Rings
• IIB horizons
• Eigenvalue estimates for multi-form modified Dirac operators
• Dynamical supersymmetry enhancement of black hole horizons