TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.111
TI  - On currents in the $O(n)$ loop model
PY  - 2024/04/24
UR  - https://scipost.org/SciPostPhys.16.4.111
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 111
A1  - Jacobsen, Jesper Lykke
AU  - Nivesvivat, Rongvoram
AU  - Saleur, Hubert
AB  - 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 $n≠ 2$), 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 \[Nucl. Phys. B 419, 411 (1994)] 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 [Nucl. Phys. B 265, 409 (1986)]. This is, to our knowledge, one of the first instances where the Coulomb gas formalism and the bootstrap can be successfully compared.
ER  -

@Article{10.21468/SciPostPhys.16.4.111,
	title={{On currents in the $O(n)$ loop model}},
	author={Jesper Lykke Jacobsen and Rongvoram Nivesvivat and Hubert Saleur},
	journal={SciPost Phys.},
	volume={16},
	pages={111},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.111},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.111},
}