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

Abstract

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 $\Sigma$ and a three-manifold $M$, and show that when $\Sigma$ 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 $\mathcal{N}=2$ superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.

26 pages. v2: the discussion on the boundary condition for vector multiplet improved, and other minor changes made

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Cited by in corpus (2)

• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory