3D-3D correspondence from Seifert fibering operators

Using recently developed Seifert fibering operators for 3D 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.

Automated summary

Using recently developed Seifert fibering operators, a state-integral model for the topological quantum field theory dual to a given Seifert manifold was formulated for 3D N = 2 gauge theories. Focus was given to Seifert homology spheres with positive orbifold Euler characteristic, and a set of difference operators were shown to annihiliate the wavefunctions of this TQFT on hyperbolic three-manifolds. These findings provide intriguing clues to the structure of the underlying TQFT.