Joerg Teschner: Fusion of the Virasoro representations in the spectrum of Liouville theory

Date: 2024-07-16

Time: 09:30 - 10:30

Speaker

Joerg Teschner, Hamburg/DESY


Abstract
A central problem in the harmonic analysis of the group of diffeomorphisms of the unit

circle is to find the analog of the Clebsch-Gordan decomposition of tensor products of

representations into irreducible representations. The appropriate notion of the tensor

product of representations is the fusion product from conformal field theory.

The goal of this talk is to formulate and motivate a conjecture on the density describing

the weight of an irreducible representation in the decomposition of the fusion product

of the Virasoro representations appearing in the spectrum of Liouville conformal field

theory. We hope that a proof of this conjecture can be achieved using the probabilistic

approach to Liouville CFT.