Conformal correlator systems — Draconitic Research

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.

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BibTeX RIS

BibTeX

@misc{ribault2026conformal,
  title = {{Conformal correlator systems}},
  author = {Sylvain Ribault},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31237},
  eprint = {2609.31237},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31237},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Conformal correlator systems
AU  - Sylvain Ribault
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31237
UR  - https://arxiv.org/abs/2609.31237
AB  - 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.
ER  -

Abstract

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