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

TL;DR

This paper classifies connected étale algebras in rank six multiplicity-free modular fusion categories, revealing only one category with nontrivial algebra and exploring implications for anyon condensation and symmetry breaking.

Contribution

It provides the first classification of connected étale algebras in rank six multiplicity-free modular fusion categories, highlighting the unique case of $so(5)_2$ and its physical applications.

Findings

Only $so(5)_2$ has nontrivial connected étale algebra among the eight categories.

Demonstrates spontaneous symmetry breaking in these categories.

Predicts ground state degeneracies and symmetry breaking in related RG flows.

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.