Classification of connected \'etale algebras in multiplicity-free modular fusion categories up to rank nine

TL;DR

This paper classifies connected étale algebras in certain modular fusion categories up to rank nine and explores their physical implications, including RG flows and symmetry breaking.

Contribution

It provides a complete classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine and analyzes their associated module categories.

Findings

Classification of étale algebras up to rank nine

Identification of module categories for each algebra

Application to RG flows and symmetry breaking

Abstract

We classify connected \'etale algebras $A$'s in multiplicity-free modular fusion categories $\mathcal B$'s with $\text{rank}(\mathcal B)\le9$. We also identify categories $\mathcal B_A$'s of right $A$-modules. The results have physical applications in constraining renormalization group flows. As demonstration, we study massive renormalization group flows from non-unitary minimal models to predict ground state degeneracies and prove spontaneous $\mathcal B$-symmetry breaking.