Published July 1, 2020
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The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)
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Abstract
The notion of a transparent fusion category is defined. For the Haagerup-Izumi fusion rings with G=Z_(2n+1) (the Z_3 case is the Haagerup H_3 fusion ring), the transparent property reduces the number of independent F-symbols from order O(n6) to O(n^2), rendering the pentagon identity practically solvable. Transparent fusion categories are constructed up to Z_(15), and the explicit F-symbols are compactly presented. The potential construction of categories for new families of fusion rings is discussed.
Additional Information
We are indebted to Yuji Tachikawa for bringing our attention to the Haagerup-Izumi categories, and to Matthew Titsworth for sharing the explicit F-symbols for the Haagerup H3 fusion categories. We thank Chi-Ming Chang, Terry Gannon, Tobias Osborne, YujiTachikawa and Yifan Wang for helpful comments and suggestions on the draft. This material is based upon work supported by the U.S. Department of Energy, Office of Science,Office of High Energy Physics, under Award Number DE-SC0011632. YL is supported bythe Sherman Fairchild Foundation.Attached Files
Submitted - 2007.00670.pdf
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2007.00670.pdf
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Identifiers
- Eprint ID
- 104260
- Resolver ID
- CaltechAUTHORS:20200707-153720334
Related works
- Describes
- http://arxiv.org/abs/2007.00670 (URL)
Funding
- Department of Energy (DOE)
- DE-SC0011632
- Sherman Fairchild Foundation
Dates
- Created
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2020-07-07Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2020-018