Classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911852683853824 |
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| author | Kikuchi, Ken |
| author_facet | Kikuchi, Ken |
| contents | We classify connected étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine Kikuchi, Ken Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory We classify connected étale 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. |
| title | Classification of connected étale algebras in multiplicity-free modular fusion categories up to rank nine |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2404.16125 |