Classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine

Abstract

We classify connected étale algebras $A$'s in multiplicity-free modular fusion categories $\mathcal{B}$'s with $\text{rank}(\mathcal{B})\le 9$. 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.

142 pages, 1 figure