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October, 2018 Vertex operator algebras, minimal models, and modular linear differential equations of order 4
Yusuke ARIKE, Kiyokazu NAGATOMO, Yuichi SAKAI
J. Math. Soc. Japan 70(4): 1347-1373 (October, 2018). DOI: 10.2969/jmsj/74957495

Abstract

In this paper we classify vertex operator algebras with three conditions which arise from Virasoro minimal models: (A) the central charge and conformal weights are rational numbers, (B) the space spanned by characters of all simple modules of a vertex operator algebra coincides with the space of solutions of a modular linear differential equation of order $4$ and (C) the dimensions of first three weight subspaces of a VOA are $1, 0$ and $1$, respectively. It is shown that vertex operator algebras which we concern have central charges $c=-46/3, -3/5, -114/7, 4/5$, and are isomorphic to minimal models for $c=-46/3, -3/5$ and ${\mathbb{Z}}_2$-graded simple current extensions of minimal models for $c=-114/7, 4/5$.

Funding Statement

The first author was supported by JSPS KAKENHI Grant Number 25800003. The second author was partially supported by JSPS KAKENHI Grant Number 17K04171, International Center of Theoretical Physics, Italy, and Max Planck institute for Mathematics, Germany. The third author was partially supported by JSPS KAKENHI Grant Numbers 15K13428 and 16H06336.

Citation

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Yusuke ARIKE. Kiyokazu NAGATOMO. Yuichi SAKAI. "Vertex operator algebras, minimal models, and modular linear differential equations of order 4." J. Math. Soc. Japan 70 (4) 1347 - 1373, October, 2018. https://doi.org/10.2969/jmsj/74957495

Information

Received: 19 April 2016; Revised: 13 March 2017; Published: October, 2018
First available in Project Euclid: 30 August 2018

zbMATH: 07009705
MathSciNet: MR3868210
Digital Object Identifier: 10.2969/jmsj/74957495

Subjects:
Primary: 81T40
Secondary: 11F11, 17B69

Rights: Copyright © 2018 Mathematical Society of Japan

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Vol.70 • No. 4 • October, 2018
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