Work

From combinatorial maps to correlation functions in loop models

Year: 2023

Type: article

Abstract: In two-dimensional statistical physics, correlation functions of the O(N) 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 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 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) 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.

Source: SciPost Physics

DOI: 10.21468/scipostphys.15.4.147

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

Institutions: Institut de Physique Théorique, École Normale Supérieure - PSL, Sorbonne Université, Laboratoire de Physique de l'Ecole Normale Supérieure, University of Southern California

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, European Research Council

Awards: G4681100732, Conformal Field Theory: constructive aspects and integrability