Classification of connected \'etale algebras in modular fusion categories up to rank five

TL;DR

This paper classifies connected étale algebras in modular fusion categories of rank up to five, providing insights into symmetry breaking, anyon condensation, and physical applications in topological phases.

Contribution

It offers a complete classification of connected étale algebras in low-rank modular fusion categories and discusses their implications in physics.

Findings

Classification of étale algebras up to rank five

Prediction of ground state degeneracies in RG flows

Analysis of symmetry breaking and anyon condensation

Abstract

We classify connected \'etale algebras in (possibly non-unitary) modular fusion categories $\mathcal B$'s with $\text{rank}(\mathcal B)\le5$. We also comment on Lagrangian algebra, anyon condensation, and physical applications. Concretely, we prove certain spontaneous $\mathcal B$-symmetry breaking and predict ground state degeneracies in massive renormalization group flows from non-unitary minimal models.