# Chiral algebras from \Omega-deformation

## TL;DR

This paper demonstrates that in 4D N=2 supersymmetric theories, the chiral algebra generated by local operators under Omega-deformation aligns with Beem et al.'s construction, extending to nonconformal cases with surface defects.

## Contribution

It establishes a precise correspondence between the Omega-deformation induced chiral algebra and Beem et al.'s algebra for unitary N=2 superconformal theories, including nonconformal cases with defects.

## Key findings

- Chiral algebra matches Beem et al.'s construction in superconformal case.
- Extension of chiral algebra definition to nonconformal theories with surface defects.
- Provides a unified framework for chiral algebras in supersymmetric theories.

## Abstract

In the presence of an $\Omega$-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional $\mathcal{N} = 2$ supersymmetric field theory. We show that for a unitary $\mathcal{N} = 2$ superconformal field theory, the chiral algebra thus defined is isomorphic to the one introduced by Beem et al. Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects.