Index theory and dynamical symmetry enhancement of M-horizons

Abstract

We show that near-horizon geometries of 11-dimensional supergravity preserve an even number of supersymmetries. The proof follows from Lichnerowicz type theorems for two horizon Dirac operators, the field equations and Bianchi identities, and the vanishing of the index of a Dirac operator on the 9-dimensional horizon sections. As a consequence of this, we also prove that all M-horizons with non-vanishing fluxes admit a sl(2,R) subalgebra of symmetries.

Minor typos corrected. 22 pages, latex. Repeats equations and descriptions from arXiv:1207.7086

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• Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces
• IIB black hole horizons with five-form flux and KT geometry
• Static M-horizons
• IIB black hole horizons with five-form flux and extended supersymmetry
• M-Horizons
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• Index theory and dynamical symmetry enhancement near IIB horizons
• Dynamical symmetry enhancement near IIA horizons
• The Near-Horizon Geometry of Supersymmetric Rotating AdS${}_4$ Black Holes in M-theory
• Dynamical symmetry enhancement near massive IIA horizons
• Anomaly Corrected Heterotic 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
• N=4 Near-Horizon Geometries in D=11 Supergravity
• Supersymmetric dS4 solutions in D=11 supergravity
• Extremal Black Holes from Homotopy Algebras
• Supersymmetry Enhancement of Heterotic Horizons
• Spinorial geometry, horizons and superconformal symmetry in six dimensions
• $D=11$ $d{S}_5$ backgrounds with enhanced supersymmetry