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.

arXiv comment26 pages. v2: the discussion on the boundary condition for vector multiplet improved, and other minor changes made

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• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• SCFT/VOA correspondence via $\Omega$-deformation
• A slow review of the AGT correspondence
• Chiral algebras from Ω-deformation
• Quiver gauge theories and integrable lattice models
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Superspin chains from superstring theory
• Integrable 3D lattice model in M-theory
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• 5d-4d Correspondence in Twisted M-theory on a Conifold