Proceedings of the Japan Academy, Series A, Mathematical Sciences

Vertex operator algebras with central charge 1/2 and $-68/7$

Kiyokazu Nagatomo and Yuichi Sakai

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In this article we study \textit{simple vertex operator algebras} whose spaces of characters are 3-dimensional, and satisfy \textit{3rd order (modular) linear differential equations}. We classify such vertex operator algebras with central charge 1/2 or $-68/7$. One of the main results is that these vertex operator algebras have \textit{conformal weights} $\{0,1/2,1/16\}$ or $\{0,-2/7,-3/7\}$, respectively, and are isomorphic to the minimal models of central charge $c=c_{3,4}=1/2$ and $c_{2,7}=-68/7$. Moreover, we give the explicit formulas representing characters of the minimal models with $c=1/2$, $-68/7$ by using the classical Weber functions.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 2 (2016), 33-37.

First available in Project Euclid: 28 January 2016

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Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight 81T40: Two-dimensional field theories, conformal field theories, etc.
Secondary: 17B69: Vertex operators; vertex operator algebras and related structures

Vertex operator algebras classification of vertex operator algebras


Nagatomo, Kiyokazu; Sakai, Yuichi. Vertex operator algebras with central charge 1/2 and $-68/7$. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 2, 33--37. doi:10.3792/pjaa.92.33.

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