Vertex operator algebras with positive central charges whose dimensions of weight one spaces are 8 and 16

Abstract

We classify rational simple self-dual vertex operator algebras V of CFT and of finite type with positive central charges, where dV=dim⁡V1 is either 8 or 16, under the condition that the space spanned by characters of V-modules is equal to the solution space of some monic modular linear differential equation of the third order. It is shown that central charges are c=8 for dV=8, and c=4,16 for dim⁡dV=16, respectively. In fact, under the condition that V1 equipped with the 0th product of V are abelian Lie algebras for dV=8,c=8 and dV=16,c=16, the vertex operator algebras V are isomorphic to V2E8 and VΛ16, respectively. For dV=16 and c=4, V is isomorphic to the lattice vertex operator algebra VA2⊕A2.