Appears in collection : Higher Structures in Holomorphic and Topological Field Theory

There is a renewed interest in the theory of chiral algebras due to recently discovered relations to supersymmetric gauge theory. A well-studied example of such a correspondence is between the operators of the chiral Wess-Zumino-Witten model and Chern-Simons theory. We will discuss two directions of current work that provide a systematic formulation of this correspondence. The first is the realization of a wide class of vertex algebras as boundary conditions to 3d topological field theories labeled by Courant algebroids, which is joint work with P. Safronov. The second direction proposes a connection of higher dimensional chiral algebras, which were introduced in O.Gwilliam’s lecture, and gauge theories in 5 and 7 dimensions.