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Classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine (2404.16125v1)

Published 24 Apr 2024 in math.QA, hep-th, math-ph, math.CT, and math.MP

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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