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arXiv · 2305.05746

Non-invertible symmetries and RG flows in the two-dimensional $O(n)$ loop model

Jesper Lykke Jacobsen·Hubert Saleur
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Abstract

In a recent paper, Gorbenko and Zan [arXiv:2005.07708] observed that $O(n)$ symmetry alone does not protect the well-known renormalization group flow from the dilute to the dense phase of the two-dimensional $O(n)$ model under thermal perturbations. We show in this paper that the required "extra protection" is topological in nature, and is related to the existence of certain non-invertible topological defect lines. We define these defect lines and discuss the ensuing topological protection, both in the context of the $O(n)$ lattice model and in its recently understood continuum limit, which takes the form of a conformal field theory governed by an interchiral algebra.

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Jesper Lykke Jacobsen, Hubert Saleur. 2023-05-09. Non-invertible symmetries and RG flows in the two-dimensional $O(n)$ loop model. https://arxiv.org/abs/2305.05746

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