3D-3D Correspondence from Seifert Fibering Operators

Abstract

Using recently developed Seifert fibering operators for 3D $\mathcal{N}=2$ gauge theories, we formulate the necessary ingredients for a state-integral model of the topological quantum field theory dual to a given Seifert manifold under the 3D-3D correspondence, focusing on the case of Seifert homology spheres with positive orbifold Euler characteristic. We further exhibit a set of difference operators that annihilate the wavefunctions of this TQFT on hyperbolic three-manifolds, generalizing similar constructions for lens space partition functions and holomorphic blocks. These properties offer intriguing clues as to the structure of the underlying TQFT.

80 pages, comments welcome; v2: minor improvements, approximates published version

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• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Bethe/Gauge correspondence on curved spaces
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
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Cited by in corpus (1)

• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories