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arXiv · 1812.11816

An Index for Superconformal Quantum Mechanics

Nick Dorey·Andrew Singleton
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Abstract

We study quantum mechanical systems with $\mathfrak{osp}(4^{*}|4)$ superconformal symmetry. We classify unitary lowest-weight representations of this superconformal algebra and define an index which receives contributions from short and semi-short multiplets only. We consider the example of a quantum mechanical $\sigma$-model with hyper-K\"{a}hler target $\mathcal{M}$ equipped with a triholomorphic homothety. The superconformal index coincides with the Witten index of a novel form of supersymmetric quantum mechanics for a particle moving on $\mathcal{M}$ in a background magnetic field in which an unbroken $\mathfrak{su}(1|2)$ subalgebra of the superconformal algebra is linearly realised as a global symmetry.

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Nick Dorey, Andrew Singleton. 2018-12-31. An Index for Superconformal Quantum Mechanics. https://arxiv.org/abs/1812.11816

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