Poisson vertex algebras in supersymmetric field theories

A large class of supersymmetric quantum field theories, including all theories with N=2 supersymmetry in three dimensions and theories with N=2 supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional N=2 superconformal field theory, the associated Poisson vertex algebra is the classical limit of a vertex algebra generated by a subset of local operators of the theory.