From combinatorial maps to correlation functions in loop models

Sylvain Ribault

IPhT

Mon, Feb. 06th 2023, 11:00-12:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

In the two-dimensional O(n) and Potts models, some observables can be computed as weighted sums over configurations of non-intersecting loops.
I will define weighted sums associated to a large class of combinatorial maps, also known as ribbon graphs, fatgraphs or rotation systems. Given a map with $N$ vertices, this yields a function of the moduli of the corresponding punctured Riemann surface, which I will call an $N$-point correlation function.
I will conjecture that in the critical limit, such correlation functions form a basis of solutions of certain conformal bootstrap equations. They include all correlation functions of the O(n) and Potts models, and correlation functions that do not belong to any known model.
[The talk will also be streamed online, please ask the organizers for the link.]

Contact : Jeremie
BOUTTIER