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Classification of some
vertex operator algebras of rank 3
Cameron Franc and Geoffrey Mason |
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Vol. 14 (2020), No. 6, 1613–1667
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Abstract |
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We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our main theorem provides a classification of all such VOAs in the form of one infinite family of affine VOAs, one individual affine algebra and two Virasoro algebras, together with a family of eleven exceptional character vectors and associated data that we call the -series. We prove that there are at least VOAs in the -series occurring as commutants in a Schellekens list holomorphic VOA. These include the affine algebra and Höhn’s baby monster VOA but the other seem to be new. The idea in the proof of our main theorem is to exploit properties of a family of vector-valued modular forms with rational functions as Fourier coefficients, which solves a family of modular linear differential equations in terms of generalized hypergeometric series. |
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Keywords
vertex operator algebras, vector-valued modular forms,
modular linear differential equations
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Mathematical Subject Classification 2010
Primary: 17B69
Secondary: 11F03, 17B65
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Milestones
Received: 28 May 2019
Revised: 5 November 2019
Accepted: 10 February 2020
Published: 30 July 2020
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Authors |
| Cameron Franc | |
| University of Saskatchewan Saskatoon, SK Canada |
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| Geoffrey Mason | |
| University of California at Santa
Cruz Santa Cruz, CA United States |
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