References & Citations
High Energy Physics - Theory
Title: On currents in the $O(n)$ loop model
(Submitted on 17 Oct 2023 (v1), last revised 28 Mar 2024 (this version, v2))
Abstract: 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.
Submission history
From: Rongvoram Nivesvivat [view email][v1] Tue, 17 Oct 2023 08:08:48 GMT (73kb,D)
[v2] Thu, 28 Mar 2024 07:59:47 GMT (76kb,D)
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