Vertex algebras at the corner

Abstract

We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N = 4 Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of the four-dimensional gauge theory. The gauge theory construction equips the vertex algebras with collections of modules labelled by supersymmetric interface line defects. We discuss in detail the simplest class of algebras YL,M,N, which generalizes WN algebras. We uncover tantalizing relations between YL,M,N, the topological vertex and the W1+∞ algebra.