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Factorization algebras in conformal field theory

Banff International Research Station for Mathematical Innovation and Discovery

There are three intertwined schools of thought in the world of factorization algebras. First, chronologically, is the theory of Beilinson-Drinfeld in their work on chiral algebras. Next, there is the Lurie, Francis-Ayala approach which is primarily the setting in which David Jordanâ s talks are in. Finally, there are factorization algebras in the style of Costello-Gwilliam. Each of these approaches have their own advantages. In this talk, I will focus on the third option. In the topological case, the theory agrees with that of Lurie/Francis-Ayala. The primary advantage of this approach is that it is more intrinsic to the underlying geometry. In complex dimension one, for instance, there is the theory of *holomorphic* factorization algebras. We will see how this notion encodes the operator product expansion (OPE) for chiral CFT, while also providing some geometric examples. We will also see how factorization homology appears in this approach to factorization.

Mathematics; Algebraic geometry; Quantum theory; Mathematical physics

video/mp4

Author affiliation: Northeastern University

2019-03-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69132

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/