Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

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

[thumbnail of 1-s2.0-S0001870816302584-main.pdf]
Preview
PDF - Published Version
Available under License Creative Commons Attribution.

Download (818kB) | Preview

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: 05 May 2023 05:55
URI: https://orca.cardiff.ac.uk/id/eprint/73921

Citation Data

Cited 5 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics