From combinatorial maps to correlation functions in loop models
Sylvain Ribault
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.
Contact : Jeremie BOUTTIER


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