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Supersymmetry and Localization on Three-Dimensional Orbifolds

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arxiv 2312.17086 v3 pith:HLDUVOPF submitted 2023-12-28 hep-th math-phmath.MP

Matteo Inglese , Dario Martelli , Antonio Pittelli This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords theoriessigmasupersymmetricthree-dimensionalcompactifieddefinedfunctionsgauge
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abstract

We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories defined on general complex-valued backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We compute partition functions for theories defined on general circle bundles over spindles $\Sigma $, including $\Sigma \times S^1$ as well as branched and squashed lens spaces, thus obtaining novel observables characterizing three-dimensional supersymmetric gauge theories. We discuss both twisted and anti-twisted theories compactified on $\Sigma \times S^1$ and demonstrate that their partition functions are encoded by a single formula that we refer to as the \emph{spindle index}, unifying and generalizing superconformal and topologically twisted indices in the limit where orbifold singularities are absent. Furthermore, we test our new index using non-perturbative dualities and obtain one-loop determinants of two-dimensional supersymmetric gauge theories compactified on the spindle.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Equivariant localization for $D=4$ gauged supergravity

    hep-th 2024-12 conditional novelty 8.0 of 10

    Supersymmetric Euclidean D=4 N=2 gauged supergravity actions and fluxes localize onto R-symmetry fixed points, proving large-N SCFT free-energy formulas and UV-IR relations.

  2. Supersymmetric $\mathbb{WCP}^n$, AdS near horizons and orbifolds

    hep-th 2025-11 conditional novelty 7.0 of 10

    Weighted projective spaces WCP² and WCP³ can be made supersymmetric for tuned integer weights, yielding new AdS₅×WCP²×S¹, AdS₄×WCP³, and AdS₃×WT(1,1) supergravity solutions.

  3. NUTs, Bolts, and Spindles

    hep-th 2024-11 conditional novelty 7.0 of 10

    New infinite families of supersymmetric spindle-bolt solutions with branched lens-space boundaries are constructed, with on-shell actions matching equivariant localization.

  4. Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Exact partition functions for N=(2,2) theories on spindles are computed via localisation for both twist and anti-twist, yielding a unified formula.

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