A localization method for type B superconformal indices on singular spaces is proposed, with a self-adjointness caveat that can make the index ambiguous.
Superconformal Quantum Mechanics on K\"ahler Cones
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abstract
We consider supersymmetric quantum mechanics on a K\"{a}hler 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.
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Index and localization for type B superconformal mechanics on singular spaces
A localization method for type B superconformal indices on singular spaces is proposed, with a self-adjointness caveat that can make the index ambiguous.