Superconformal quantum mechanics on Kähler cones

bstract We consider supersymmetric quantum mechanics on a Kähler cone, regulated via a suitable resolution of the conical singularity. The unresolved space has a u(1 , 1 | 2) superconformal symmetry and we propose the existence of an associated quantum mechanical theory with a discrete spectrum consisting of unitary, lowest weight representations of this algebra. We define a corresponding superconformal index and compute it for a wide range of examples.