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$\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity

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arxiv 1411.2762 v3 pith:NGRSMZCH submitted 2014-11-11 hep-th math-phmath.AGmath.MPmath.RT

Aditya Bawane , Giulio Bonelli , Massimiliano Ronzani , Alessandro Tanzini This is my paper · ORCID
classification hep-thmath-phmath.AGmath.MPmath.RT
keywords supersymmetricadmittingblocksfourgaugegravityisometryliouville
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abstract

We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2\times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

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Cited by 3 Pith papers

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

  1. 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.

  2. Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes

    hep-th 2025-10 conditional novelty 6.0 of 10

    Derives a single-flux contour-integral formula for the N=2 twisted SU(2) partition function on CP^2 and new equivariant invariants reducing to Donaldson invariants.

  3. Refined Painlev\'e/gauge theory correspondence and quantum tau functions

    hep-th 2025-02 conditional novelty 6.0 of 10

    Strong-coupling expansions of N=2 SU(2) partition functions in general Omega-background are derived from quantum Painlevé equations obtained via C2/Z2 blowup relations, and match refined holomorphic anomaly and irregu...

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