  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.

High Energy Physics - Theory