3d-3d Correspondence Revisited

Abstract

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

43 pages + 1 appendix, 6 figures Version 2: new appendix on flat connections in the 3d-3d correspondence

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• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit
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• S-duality resurgence in SL(2) Chern-Simons theory
• Star shaped quivers with flux
• Intersecting Defects and Supergroup Gauge Theory
• Infrared phases of 3D Class R theories
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• (0,2) Dualities and the 4-Simplex
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• 3D-3D Correspondence from Seifert Fibering Operators
• Permutohedra for knots and quivers
• Aspects of 4d supersymmetric dynamics and geometry