The spindle index from localization

DOI10.1088/1751-8121/AD2225arXiv2303.14199OpenAlexW4391164870WikidataQ129449565 ScholiaQ129449565MaRDI QIDQ6149917

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Publication date: 5 March 2024

Published in: (Search for Journal in Brave)

Abstract: We present a new supersymmetric index for three-dimensional $calN=2$ gauge theories defined on $Sigmaimes{S}^1$, 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 $Sigmaimes{S}^1$ 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.

Full work available at URL: https://arxiv.org/abs/2303.14199

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