3d-3d Correspondence Revisited

Understand

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.