Vertex Operator Algebras with Two Simple Modules - the Mathur-Mukhi-Sen Theorem Revisited

2018/03/29 by Geoffrey Mason, Mason, Geoffrey, Kiyokazu Nagatomo +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1803.11281

Abstract

Let V be a strongly regular vertex operator algebra and let \frakch_V be the space spanned by the characters of the irreducible V-modules. It is known that \frakch_V is the space of solutions of a so-called modular linear differential equation (MLDE). In this paper we obtain a near-classification of those V for which the corresponding MLDE is irreducible and monic of order 2. As a consequence we derive the complete classification when V has exactly two simple modules. It turns out that V is either one of four affine Kac-Moody algebras of level 1, or the Yang-Lee Virasoro model of central charge -22/5. Our proof establishes new connections between the characters of V and Gauss hypergeometric series, and puts the finishing touches to work of Mathur, Mukhi and Sen who first considered this problem forty years ago.

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• Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT

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