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arXiv · 2402.00403

Classification of connected \'etale algebras in multiplicity-free modular fusion categories at rank six

Ken Kikuchi·Kah-Sen Kam·Fu-Hsiang Huang
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Abstract

We classify connected \'etale 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 \'etale 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.

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Ken Kikuchi, Kah-Sen Kam, Fu-Hsiang Huang. 2024-02-01. Classification of connected \'etale algebras in multiplicity-free modular fusion categories at rank six. https://doi.org/10.4310/atmp.260604113634

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