Classification of connected étale algebras in modular fusion categories up to rank five

Abstract

We classify connected étale algebras in (possibly non-unitary) modular fusion categories $\mathcal{B}$'s with $\text{rank}(\mathcal{B})\le 5$. 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.

32 pages + references; v2: minor corrections on Toric Code, fixed typos; v3: minor corrections on $psu(2{)}_9$, and added a theorem in section 3.1 proving modular fusion categories $\mathcal{B}$'s with $\text{rank}(\mathcal{B})>1$ are spontaneously broken; v4: minor corrections on ${\text{Vec}}_{\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}}$; v5:corrected method and typos

Cited by in corpus (2)

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