Speaker: Rongvoram Nivesvivat (Yau Center, Tsinghua U, Beijing)

Abstract: I will propose an exact formula for arbitrary structure constants of
arbitrary four-point functions in the critical O(n) loop model for
arbitrary n. The formula is a function of conformal dimensions, built
from Barnes’ double Gamma function, times a polynomial function in n.
Using the conformal bootstrap, we determine exactly this polynomial in
several examples, and conjecture a bound on its degree. To solve the
critical O(n) loop model, it remains to find an infinite family of
polynomials, and to factorize them in terms of three-point functions.

Besides the new results, this talk will also cover a brief
introduction to the critical O(n) loop model, as well as some basic
ideas of the conformal bootstrap.

This talk is based on upcoming papers with Jesper Jacobsen, Sylvain
Ribault, and Hubert Saleur.