Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six

We classify connected étale algebras \(A\)'s in multiplicity-free modular fusion categories (MFCs) \(\mathcal{B}\)'s at rank six, namely \(\text{rank}(\mathcal{B})=6\). There are eight MFCs in total and the result indicates that only \(so(5)_2\) has nontrivial connected étale algebra. We b...

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Bibliographic Details
Published inarXiv.org
Main Authors Kikuchi, Ken, Kah-Sen, Kam, Fu-Hsiang, Huang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.02.2024
Subjects
Algebra
Broken symmetry
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Summary:We classify connected étale algebras \(A\)'s in multiplicity-free modular fusion categories (MFCs) \(\mathcal{B}\)'s at rank six, namely \(\text{rank}(\mathcal{B})=6\). There are eight MFCs in total and the result indicates that only \(so(5)_2\) has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right \(A\)-modules in \(so(5)_2\). Finally, we discuss physical applications, specifically proving spontaneous \(\mathcal{B}\)-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models.
ISSN:2331-8422