| Summary: | Abstract We explore aspects of the correspondence between Seifert 3-manifolds and 3d N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 2 theories constructed from boundary conditions and interfaces in a 4d N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 2∗ theory. In the presence of a mass parameter cfor the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.
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