Comments on chiral algebras and $\Omega$-deformations

TL;DR

This paper presents an alternative method to construct the chiral algebra associated with 6D $ ext{(2,0)}$ SCFTs using $oldsymbol{ ext{Ω}}$-deformation and cohomology, linking central charge to anomaly polynomial integration.

Contribution

It introduces a new construction of the chiral algebra via $oldsymbol{ ext{Ω}}$-deformation of a topological-holomorphic twist and extends the framework to orbifolds of the transverse space.

Findings

Constructed the chiral algebra through $oldsymbol{ ext{Ω}}$-deformation and supercharge cohomology.

Connected the chiral algebra's central charge to equivariant integration of the anomaly polynomial.

Generalized the construction to include orbifolds of the transverse space.

Abstract

Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. We provide an alternative construction of this chiral algebra by performing an $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on $\mathbf{R}^6$ and restricting to the cohomology of a specific supercharge. In addition, we show that the central charge of the chiral algebra can be obtained by performing equivariant integration of the anomaly polynomial of the six-dimensional theory. Furthermore, we generalize this construction to include orbifolds of the $\mathbf{R}^4$ transverse to the chiral algebra plane.