On the six-dimensional origin of the AGT correspondence

TL;DR

This paper explores how a six-dimensional superconformal theory, when twisted, reveals a W-algebra structure in its chiral algebra, connecting higher-dimensional theories to algebraic structures in lower dimensions.

Contribution

It proposes a specific twisting of the six-dimensional (2,0) theory that leads to a W-algebra in the chiral algebra, advancing understanding of the AGT correspondence.

Findings

W-algebra appears in the chiral algebra of the twisted theory

The structure persists under -deformation

The theory is topological on M and holomorphic on C

Abstract

We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R^4, possibly in the presence of a codimension-two defect operator supported on R^2 \times C \subset M \times C. We expect this structure to survive the \Omega-deformation.