Vertex algebras at the corner

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 Y-L,Y-M,Y-N, which generalizes W-N algebras. We uncover tantalizing relations between Y-L,Y-M,Y-N, the topological vertex and the W1+ algebra.