Vertex algebras at the corner

A bstract We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N 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 Y L,M,N , which generalizes W N algebras. We uncover tantalizing relations between Y L,M,N , the topological vertex and the W 1+∞ algebra.