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Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
by Kansei Inamura, Kantaro Ohmori
Submission summary
| Authors (as registered SciPost users): | Kansei Inamura · Kantaro Ohmori |
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| Preprint Link: | scipost_202402_00032v1 (pdf) |
| Date submitted: | 2024-02-22 07:08 |
| Submitted by: | Inamura, Kansei |
| Submitted to: | SciPost Physics Core |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the "symmetry TFTs" for fusion 2-category symmetries play an important role.
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Report
Regarding item 6 of Report 1, it is not true in general that a "Δ-separable Frobenius algebra in a pivotal fusion category is automatically symmetric". For example, the cited reference by Fuchs-Runkel-Schweigert proves symmetry under the additional assumptions "sovereign" and "haploid". The symmetry condition can be thought of as a compatibility condition between the ambient structure of and on adjoints (here: pivotality) and the underlying condensation monad. Such compatibilities also appear in higher dimensions and constitute the main difference between condensation monads and orbifold data.