Index theory and dynamical symmetry enhancement of M-horizons

TL;DR

This paper proves that near-horizon geometries in 11-dimensional supergravity preserve an even number of supersymmetries and exhibit an sl(2,R) symmetry subalgebra, using index theory and Dirac operator analysis.

Contribution

It introduces a novel proof that all M-horizons with fluxes have even supersymmetries and an sl(2,R) symmetry, based on Lichnerowicz theorems and index calculations.

Findings

All M-horizons preserve an even number of supersymmetries.

M-horizons with fluxes admit an sl(2,R) symmetry subalgebra.

The proof employs Dirac operator index theory and horizon geometry analysis.

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.