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

Ken Kikuchi

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arXiv · 2312.13353

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

Ken Kikuchi

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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.

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Ken Kikuchi. 2023-12-20. Classification of connected \'etale algebras in modular fusion categories up to rank five. https://arxiv.org/abs/2312.13353

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