We introduce a class of Vertex Operator Algebras which arise at junctions of
supersymmetric interfaces in ${\cal N}=4$ 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 $W_{1+\infty}$ algebra.