SciPost Physics Core

SciPost Phys. Core 6, 020 (2023) · published 27 March 2023

• doi: 10.21468/SciPostPhysCore.6.1.020
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Abstract

In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$ weights of topologically inequivalent loops on a sphere with $N$ punctures. Using a numerical conformal bootstrap approach, we find that $4$-point functions decompose into infinite but discrete linear combinations of conformal blocks. We conclude that diagonal fields belong to an extension of the $O(n)$ model.

• Jacobsen et al., Non-invertible symmetries and RG flows in the two-dimensional O(n) loop model
  J. High Energ. Phys. 2023, 90 (2023) [Crossref]
• Nivesvivat et al., Critical loop models are exactly solvable
  SciPost Phys. 17, 029 (2024) [Crossref]
• Grans-Samuelsson et al., From combinatorial maps to correlation functions in loop models
  SciPost Phys. 15, 147 (2023) [Crossref]