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.

We prove that Killing horizons in massive IIA supergravity preserve an even number of supersymmetries, and that their symmetry algebra contains an sl(2, R) subalgebra, confirming the conjecture of [5]. We also prove a new class of Lichnerowicz type theorems for connections of the spin bundle whose holonomy is contained in a general linear group.

We consider the near-horizon geometry of supersymmetric extremal black holes in ungauged and gauged 5-dimensional supergravity, coupled to abelian vector multiplets. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a supersymmetry enhancement. This follows from a set of generalized Lichnerowicz-type theorems we establish, together with an index theory argument. As a consequence, these solutions always admit a sl(2, R) symmetry group.