String-Math Seminar: Extensions of Kac-Moody algebras and Calabi-Yau singularities

Seminar | September 30 | 2-3 p.m. | 402 LeConte Hall

 Miroslav Rapcak, UC Berkeley

 Department of Mathematics

We discuss a class of vertex operator algebras $\mathcal W_{m|n\times \infty }$ 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 $xy=z^mw^n$. We 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.