Dynamical symmetry enhancement near IIA horizons

TL;DR

This paper proves that smooth type IIA Killing horizons with compact sections preserve an even number of supersymmetries and include an sl(2,R) symmetry, confirming a prior conjecture and introducing new mathematical theorems.

Contribution

It establishes supersymmetry preservation and symmetry algebra structure for type IIA horizons, and proves new Lichnerowicz type theorems for spin bundle connections.

Findings

Horizons preserve an even number of supersymmetries

Symmetry algebra includes an sl(2,R) subalgebra

Confirmed the conjecture for type IIA horizons

Abstract

We show that smooth type IIA Killing horizons with compact spatial sections preserve an even number of supersymmetries, and that the symmetry algebra of horizons with non-trivial fluxes includes an sl(2,R) subalgebra. This confirms the conjecture of [1] for type IIA horizons. As an intermediate step in the proof, we also demonstrate new Lichnerowicz type theorems for spin bundle connections whose holonomy is contained in a general linear group.