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Article Dans Une Revue SciPost Physics Année : 2022

Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model

Résumé

We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we write a conjecture for the decomposition of the spectrum into irreducible representations of $O(n)$. We then explain how to numerically bootstrap arbitrary four-point functions of primary fields in the presence of the global $O(n)$ symmetry. We determine the needed conformal blocks, including logarithmic blocks, including in singular cases. We argue that $O(n)$ representation theory provides upper bounds on the number of solutions of crossing symmetry for any given four-point function. We study some of the simplest correlation functions in detail, and determine a few fusion rules. We count the solutions of crossing symmetry for the $30$ simplest four-point functions. The number of solutions varies from $2$ to $6$, and saturates the bound from $O(n)$ representation theory in $21$ out of $30$ cases.

Dates et versions

hal-03433083 , version 1 (17-11-2021)

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Linnea Grans-Samuelsson, Rongvoram Nivesvivat, Jesper Lykke Jacobsen, Sylvain Ribault, Hubert Saleur. Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model. SciPost Physics, 2022, 12 (5), pp.147. ⟨10.21468/SciPostPhys.12.5.147⟩. ⟨hal-03433083⟩
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