Refined 3d-3d correspondence

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N - 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N - 2 theories constructed from boundary conditions and interfaces in a 4d N - 2* theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2* theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of re fi ned Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S -matrix of re fi ned Chern-Simons theory.