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High Energy Theory Seminar

Friday, October 18, 2019
11:00am to 12:00pm
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Lauritsen 469
Extensions of Kac-Moody algebras and Calabi-Yau singularities.
Miroslav RapĨak, UC Berkeley,

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.

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