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The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)

Huang, Tzu-Chen and Lin, Ying-Hsuan (2020) The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1). . (Submitted)

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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.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Lin, Ying-Hsuan0000-0001-8904-1287
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.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
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Record Number:CaltechAUTHORS:20200707-153720334
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104260
Deposited By: Joy Painter
Deposited On:07 Jul 2020 23:14
Last Modified:02 Jun 2023 01:08

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