Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence

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We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface Σ and a three-manifold M, and show that when Σ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on M. Based on these results, we establish a correspondence between three-dimensional N = 2 superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.