Vertex operator algebras, minimal models, and modular linear differential equations of order 4

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 ℤ₂-graded simple current extensions of minimal models for 𝑐 = −114/7, 4/5.