Non-invertible symmetries and selection rules for RG flows of coset models

TL;DR

This paper develops a method to classify superselection sectors and topological defect lines in 2D conformal field theories, providing new insights into RG flow selection rules for coset and parafermion models.

Contribution

It introduces a novel approach based on local data to classify submodels and superselection sectors, unifying and extending existing knowledge on RG flow selection rules in CFT2.

Findings

Explicit classification of submodels in coset and parafermion models

Unified framework for selection rules in RG flows

Discovery of new aspects of RG flow behavior

Abstract

We analyze superselection sectors, non-invertible symmetries and selection rules for RG flows triggered via perturbations of a UV two-dimensional conformal field theory (CFT$_2$). To this end we describe a method whose input is the local data, and whose output is the set of submodels of the modular invariant completions. We explain how this output set provides a classification of superselection sectors (DHR categories and Q-systems) and of topological defect lines, leading to a unified and potentially complete approach to selection rules for RG flows. This method is applied to scenarios in which the UV is a coset or a parafermion model. For these CFT$_2$ we explicitly find all submodels of the diagonal modular invariants. Our results gives selection rules that unify several known facts about such RG flows, while also allowing us to find new aspects.