Conformal Bootstrap for Liouville Conformal Field Theory

Antti Kupiainen (U Helsinki)

Oct 16. 2020, 14:15 — 15:00

A. Polyakov introduced Liouville Conformal Field theory (LCFT)  in 1981 as a way to 
put a natural measure on the set of Riemannian metrics over a  two dimensional 
manifold. Ever since, the work of Polyakov has echoed in various branches of physics 
and mathematics, ranging from string theory to probability theory and geometry. 
In the context of 2D quantum gravity models, Polyakov’s approach is conjecturally 
equivalent to the scaling limit of Random Planar Maps and through the Alday-Gaiotto-
Tachikava correspondence  LCFT is conjecturally 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).

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation - partially postponed (Online Workshop)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)