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Letters in Mathematical Physics

, Volume 107, Issue 12, pp 2189–2237 | Cite as

The Virasoro vertex algebra and factorization algebras on Riemann surfaces

  • Brian WilliamsEmail author
Article
First Online:

Abstract

This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello–Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta–gamma system using the method of effective BV quantization.

Keywords

Factorization algebras Virasoro vertex algebra BV quantization Conformal field theory 

Mathematics Subject Classification

81R10 17B65 18G55 
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Notes

Acknowledgements

I’d like to thank Owen Gwilliam and Ryan Grady for their shared interest in this project and generosity in providing detailed comments and discussion pertaining to this work. I have also benefited from useful comments from and discussions with Chris Elliott, Ben Knudsen, and Philsang Yoo. Finally, I’d like to thank Kevin Costello for sparking my interest in this project.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Northwestern UniversityEvanstonUSA

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