3D-3D Correspondence from Seifert Fibering Operators

TL;DR

This paper develops a state-integral model for a 3D topological quantum field theory associated with Seifert manifolds, using Seifert fibering operators, and explores difference operators that annihilate its wavefunctions.

Contribution

It introduces a formulation of the TQFT dual to Seifert manifolds using Seifert fibering operators and constructs difference operators for hyperbolic three-manifolds, extending previous work.

Findings

Formulated a state-integral model for the 3D-3D correspondence.

Constructed difference operators for hyperbolic three-manifolds.

Provided insights into the structure of the underlying TQFT.

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.