Superconformal Quantum Mechanics on Kähler Cones

Abstract

We consider supersymmetric quantum mechanics on a Kähler cone, regulated via a suitable resolution of the conical singularity. The unresolved space has a $\mathfrak{u}(1,1|2)$ 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.

arXiv comment49 pages, 6 figures; references added

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Cited by in corpus (5)

• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• The geometry of gauged (super)conformal mechanics
• Index and localization for type B superconformal mechanics on singular spaces
• Quantum causality in $\kappa$-Minkowski and related constraints