Modular bootstrap, Segal axioms and resolution of Liouville field theory

https://hu-berlin.zoom.us/j/61686623112
Contact: Gaetan Borot

I’ll explain some ongoing joint work with Kupiainen, Rhodes and Vargas where we show that the correlation functions of Liouville conformal field theory on Riemann surfaces can be expressed purely in terms of products of 3-point functions on the sphere and the conformal blocks, which are holomorphic functions on the moduli space of punctured Riemann surfaces. The proof is strongly based on the decomposition of the path integral (written as an expectation of some random variables) into path integrals over surfaces with boundaries (building blocks/pairs of pants), which is a verification of Segal axioms in our setting, and on the spectral analysis of a certain self-adjoint Hamiltonian.