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

摘要

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 Z_2-graded simple current extensions of minimal models for c = -114/7, 4/5.