Classification of connected \'etale algebras in multiplicity-free modular fusion categories up to rank nine

Ken Kikuchi

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arXiv · 2404.16125

Classification of connected \'etale algebras in multiplicity-free modular fusion categories up to rank nine

Ken Kikuchi

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Abstract

We classify connected \'etale algebras $A$'s in multiplicity-free modular fusion categories $\mathcal B$'s with $\text{rank}(\mathcal B)\le9$. 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.

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Ken Kikuchi. 2024-04-24. Classification of connected \'etale algebras in multiplicity-free modular fusion categories up to rank nine. https://arxiv.org/abs/2404.16125

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