N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$

Abstract

We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2\times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on $S^4$.

49 pages, refs added, the final version to appear in JHEP

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Cited by in corpus (14)

• Topologically twisted indices in five dimensions and holography
• Higher Form Symmetries of Argyres-Douglas Theories
• Twisting with a Flip (the Art of Pestunization)
• Supersymmetric Rényi Entropy and Defect Operators
• Transversally Elliptic Complex and Cohomological Field Theory
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• SYM on Quotients of Spheres and Complex Projective Spaces
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• S-duality and supersymmetry on curved manifolds
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• (1,0) gauge theories on the six-sphere
• Gauge theories on spheres with 16 supercharges and non-constant couplings