TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.4.147
TI  - From combinatorial maps to correlation functions in loop models
PY  - 2023/10/09
UR  - https://scipost.org/SciPostPhys.15.4.147
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 4
SP  - 147
A1  - Grans-Samuelsson, Linnea
AU  - Jacobsen, Jesper Lykke
AU  - Nivesvivat, Rongvoram
AU  - Ribault, Sylvain
AU  - Saleur, Hubert
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.4.147,
	title={{From combinatorial maps to correlation functions in loop models}},
	author={Linnea Grans-Samuelsson and Jesper Lykke Jacobsen and Rongvoram Nivesvivat and Sylvain Ribault and Hubert Saleur},
	journal={SciPost Phys.},
	volume={15},
	pages={147},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.4.147},
	url={https://scipost.org/10.21468/SciPostPhys.15.4.147},
}