Rational RG flow, extension, and Witt class
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909990532415488 |
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| author | Kikuchi, Ken |
| author_facet | Kikuchi, Ken |
| contents | Consider a renormalization group flow preserving a pre-modular fusion category $\mathcal S_1$. If it flows to a rational conformal field theory, the surviving symmetry $\mathcal S_1$ flows to a pre-modular fusion category $\mathcal S_2$ with monoidal functor $F:\mathcal S_1\to\mathcal S_2$. By clarifying mathematical (especially category theoretical) meaning of renormalization group domain wall/interface or boundary condition, we find the hidden extended vertex operator (super)algebra gives a unique (up to braided equivalence) completely $(\mathcal S_1\boxtimes\mathcal S_2)'$-anisotropic representative of the Witt equivalence class $[\mathcal S_1\boxtimes\mathcal S_2]$. The mathematical conjecture is supported physically, and passes various tests in concrete examples including non/unitary minimal models, and Wess-Zumino-Witten models. In particular, the conjecture holds beyond diagonal cosets.
The picture also establishes the conjectured half-integer condition, which fixes infrared conformal dimensions mod $\frac12$. It further leads to the double braiding relation, namely braiding structures jump at conformal fixed points. As an application, we solve the flow from the $E$-type minimal model $(A_{10},E_6)\to M(4,3)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational RG flow, extension, and Witt class Kikuchi, Ken High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra Consider a renormalization group flow preserving a pre-modular fusion category $\mathcal S_1$. If it flows to a rational conformal field theory, the surviving symmetry $\mathcal S_1$ flows to a pre-modular fusion category $\mathcal S_2$ with monoidal functor $F:\mathcal S_1\to\mathcal S_2$. By clarifying mathematical (especially category theoretical) meaning of renormalization group domain wall/interface or boundary condition, we find the hidden extended vertex operator (super)algebra gives a unique (up to braided equivalence) completely $(\mathcal S_1\boxtimes\mathcal S_2)'$-anisotropic representative of the Witt equivalence class $[\mathcal S_1\boxtimes\mathcal S_2]$. The mathematical conjecture is supported physically, and passes various tests in concrete examples including non/unitary minimal models, and Wess-Zumino-Witten models. In particular, the conjecture holds beyond diagonal cosets. The picture also establishes the conjectured half-integer condition, which fixes infrared conformal dimensions mod $\frac12$. It further leads to the double braiding relation, namely braiding structures jump at conformal fixed points. As an application, we solve the flow from the $E$-type minimal model $(A_{10},E_6)\to M(4,3)$. |
| title | Rational RG flow, extension, and Witt class |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2412.08935 |