The spindle index from localization

Abstract

Abstract We present a new supersymmetric index for three-dimensional N = 2 gauge theories defined on Σ × S 1 , 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 × 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.