Abstract
We present a new supersymmetric index for three-dimensional N=2 gauge theories defined on Σ×S1 , where Σ 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 Σ×S1 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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