Title: Proof of the DOZZ Formula
Abstract:
In 1994 Dorn and Otto and in 1996 independently Zamolodchikov and
Zamolodchikov proposed a remarkable explicit expression, the so called DOZZ
formula for the 3 point structure constants of the Liouville Conformal Field
Theory (LCFT). LCFT is a building block of non-critical string theory and
two dimensional quantum gravity and the DOZZ formula is the key to its
integrability. Remarkably the LCFT strucure constants also give the Nekrason
partition functions of four dimensional gauge theories. I will review a
rigorous probabilistic construction of LCFT and sketch a proof of the DOZZ
formula obtained together with R. Rhodes and V. Vargas.