Classification of connected étale algebras in pre-modular fusion categories up to rank three

Abstract

We classify connected étale algebras $A$'s in pre-modular fusion categories $\mathcal{B}$ with $\text{rank}(\mathcal{B})\le 3$ including degenerate and non-(pseudo-)unitary ones. We comment on Lagrangian algebras and physical applications to ground state degeneracy and proof of spontaneous $\mathcal{B}$-symmetry breaking.

25 pages + 2 Appendices; v2: proved all $psu(2{)}_5$'s are completely anisotropic and fixed typos; v3: corrected method and typos, and completed classifications by relaxing assumption on multiplicity

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