High Energy Theory Seminar

I will discuss a class of vertex operator algebras generated by a super-matrix of fields for each integral spin 1,2,3,\dots. The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to xy=z^mw^n. I propose a free-field realization of such truncations generalizing the Miura transformation for \mathcal{W}_N algebras. Relations in the ring of holomorphic functions lead to bosonization-like relations between different free-field realizations. The discussion provides a concrete example of a non-trivial interplay between vertex operator algebras, algebraic geometry and gauge theory.