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Mathematical Physics Seminar

Antti Kupiainen - Conformal Bootstrap in Liouville Theory

Antti Kupiainen

Location:  Zoom Webinar
Date & time: Wednesday, 14 October 2020 at 10:45AM - 11:45PM

Antti Kupiainen– University of Helsinki

Wednesday, October 14, 10:45AM


"Conformal Bootstrap in Liouville Theory"

A. Polyakov introduced Liouville Conformal Field theory (LCFT)  in 1981 as a building block of non-critical string theory. Ever since, the work of Polyakov has echoed in various branches of physics and mathematics.  In the context of 2D quantum gravity models LCFT describes the scaling limit of spin systems on random lattices and through the Alday-Gaiotto-Tachikava correspondence  LCFT is related to certain 4D Yang-Mills theories.  Through  the work of Dorn,Otto, Zamolodchikov and  Zamolodchikov and Teschner LCFT is believed to be to a certain extent integrable.

I will review a probabilistic construction of LCFT developed together with David, Rhodes and Vargas and recent proofs concerning the integrability of LCFT:

-The proof  in a joint work with Rhodes and Vargas of the DOZZ formula (Annals of Mathematics, 81-166,191 (2020) -The proof  in a joint work with Guillarmou, Rhodes and Vargas of the bootstrap conjecture for LCFT (arXiv:2005.11530). 

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