Work

Conformal correlator systems

Year: 2026

Type: preprint

Abstract: In critical limits of statistical models, there exist non-local correlators that are conformally covariant without belonging to a conformal field theory. To describe such correlators, we define conformal correlator systems, whose axioms are weaker than those of CFT. As a result, $N$-point correlators are determined by $4$-point correlators, instead of $3$-point correlators in CFT. In two dimensions, conformal spins may take arbitrary complex values, leading to correlators with nontrivial monodromies. We show that sphere $4$-point correlators and torus $1$-point correlators obey nontrivial monodromy constraints. We construct correlators with abelian monodromies in free bosonic theories and in critical loop models.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31237

Author: Ribault, Sylvain

Institutions: Centre National de la Recherche Scientifique, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214647840

Cites: 14

Cited by: 1

Related to: 10