The Spindle Index from Localization

Abstract

We present a new supersymmetric index for three-dimensional $\mathcal{N}=2$ 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.

5 pages, v3: published version

References in corpus (5)

• Generalized Superconformal Index for Three Dimensional Field Theories
• Thermodynamics of accelerating and supersymmetric $Ad{S}_4$ black holes
• Supersymmetric spindles
• D4-branes wrapped on a spindle
• Supersymmetry and Localization on Three-Dimensional Orbifolds

Cited by in corpus (10)

• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• Toric gravitational instantons in gauged supergravity
• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
• Holographic Generalised Gukov-Witten Defects
• NUTs, Bolts, and Spindles
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• Branes wrapped on quadrilaterals
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle