On currents in the $O(n)$ loop model - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

On currents in the $O(n)$ loop model

Résumé

Using methods from the conformal bootstrap, we study the properties of Noether currents in the critical $O(n)$ loop model. We confirm that they do not give rise to a Kac-Moody algebra (for $n\neq 2$), a result expected from the underlying lack of unitarity. By studying four-point functions in detail, we fully determine the current-current OPEs, and thus obtain several structure constants with physical meaning. We find in particular that the terms $:\!J\bar{J}\!:$ in the identity and adjoint channels vanish exactly, invalidating the argument made in \cite{car93-1} that adding orientation-dependent interactions to the model should lead to continuously varying exponents in self-avoiding walks. We also determine the residue of the identity channel in the $JJ$ two-point function, finding that it coincides both with the result of a transfer-matrix computation for an orientation-dependent correlation function in the lattice model, and with an earlier Coulomb gas computation of Cardy \cite{car93}. This is, to our knowledge, one of the first instances where the Coulomb gas formalism and the bootstrap can be successfully compared.

Dates et versions

hal-04439609 , version 1 (05-02-2024)

Identifiants

Citer

Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Hubert Saleur. On currents in the $O(n)$ loop model. 2024. ⟨hal-04439609⟩
3 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More