## From combinatorial maps to correlation functions in loop models

Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur

SciPost Phys. 15, 147 (2023) · published 9 October 2023

- doi: 10.21468/SciPostPhys.15.4.147
- Submissions/Reports

### Abstract

In two-dimensional statistical physics, correlation functions of the $O(N)$ and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as ribbon graphs). We allow disconnected maps, but not maps that include monogons. Given a map with $n$ vertices, we obtain a function of the moduli of the corresponding punctured Riemann surface. Due to the map's combinatorial (rather than topological) nature, that function is single-valued, and we call it an $n$-point correlation function. We conjecture that in the critical limit, such 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. We test the conjecture by counting solutions of crossing symmetry for four-point functions on the sphere.

### Cited by 3

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Linnea Grans-Samuelsson, -
^{1}^{2}^{3}Jesper Lykke Jacobsen, -
^{1}Rongvoram Nivesvivat, -
^{1}Sylvain Ribault, -
^{1}^{4}Hubert Saleur

^{1}L'Institut de physique théorique [IPhT]^{2}Sorbonne Université / Sorbonne University^{3}Laboratoire de Physique de l’École Normale Supérieure / Physics Laboratory of the École Normale Supérieure [LPENS]^{4}University of Southern California [USC]