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

Abstract

A bstract In a recent paper, Gorbenko and Zan [1] 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.

Topics & Concepts