Abstract
We explore aspects of the correspondence between Seifert 3-manifolds and 3d \( \mathcal{N} \) = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d \( \mathcal{N} \) = 2 theories constructed from boundary conditions and interfaces in a 4d \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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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Alday, L.F., Genolini, P.B., Bullimore, M. et al. Refined 3d-3d correspondence. J. High Energ. Phys. 2017, 170 (2017). https://doi.org/10.1007/JHEP04(2017)170
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DOI: https://doi.org/10.1007/JHEP04(2017)170