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arXiv · 2303.14199

The Spindle Index from Localization

Matteo Inglese·Dario Martelli·Antonio Pittelli
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Abstract

We present a new supersymmetric index for three-dimensional ${\cal N}=2$ gauge theories defined on $\Sigma \times S^1$, where $\Sigma$ is a spindle, with twist or anti-twist for the $R$-symmetry background gauge field. We start examining general supersymmetric backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We then focus on $\Sigma \times S^1$ and demostrate how to realise twist and anti-twist. We compute the supersymmetric partition functions on such backgrounds via localization and show that these are captured by a general formula, depending on the type of twist, which unifies and generalises the superconformal and topologically twisted indices.

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Matteo Inglese, Dario Martelli, Antonio Pittelli. 2023-03-24. The Spindle Index from Localization. https://doi.org/10.1088/1751-8121/ad2225

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