Non-unitary fusion categories and their doubles via endomorphisms

Evans, David E. and Gannon, Terry 2017. Non-unitary fusion categories and their doubles via endomorphisms. Advances in Mathematics 310 , pp. 1-43. 10.1016/j.aim.2017.01.015

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Abstract

We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup-Izumi family of Q-systems. For example, we construct endomorphism realisations of the (non-unitary) Yang-Lee model, and non-unitary analogues of one of the even subsystems of the Haagerup subfactor and of the Grossman-Snyder system. We supplement Izumi's equations for identifying the half-braidings, which were incomplete even in his Q-system setting. We conjecture a remarkably simple form for the modular S and T matrices of the doubles of these fusion categories. We would expect all of these doubles to be realised as the category of modules of a rational VOA and conformal net of factors. We expect our approach will also suffice to realise the non-semisimple tensor categories arising in logarithmic conformal field theories.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Modular tensor categories; Non-unitary; Leavitt algebra; Quantum double; Conformal field theory; Subfactor
Additional Information:	This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Publisher:	Elsevier
ISSN:	0001-8708
Funders:	EPSRC
Date of First Compliant Deposit:	6 February 2017
Date of Acceptance:	17 January 2017
Last Modified:	04 Jul 2024 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/73921

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