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

TL;DR

This paper explores the eformation of B-twisted gauge theories, constructing a 5D theory related to Chern-Simons theory, and establishing a 3d-3d correspondence and mirror symmetry in this context.

Contribution

It introduces a novel eformation framework for B-twisted theories, linking 2D and 5D theories to Chern-Simons and 3D superconformal theories, and reveals a mirror symmetry.

Findings

eformed 5D maximally supersymmetric Yang-Mills theory on nd a three-manifold is constructed.

The theory with isk as rane reduces to analytically continued Chern-Simons theory.

A correspondence between 3D  superconformal theories and Chern-Simons theory is established.

Abstract

We study \Omega-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an \Omega-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 {\Omega}-deformed two-dimensional theories.