Masahiko Miyamoto

Modular invariance of vertex operator algebras satisfying

We show that C_2-cofiniteness is enough to prove a modular invariance property of vertex operator algebras without assuming the semisimplicity of Zhu algebra. For example, if a VOA V=\oplus_{m=0}^{\infty}V_m is C_2-cofinite, then the space spanned by generalized characters of V-modules is invariant under the action of SL_2(\Z). In this case, the central charge and conformal weights are all rational numbers. Namely, a VOA satisfying C_2-cofiniteness is a rational conformal field theory in a sense. We also show that C_2-cofiniteness is equivalent to the condition that every weak module is an \N-graded weak module which is a direct sum of generalized eigenspaces of L(0).

C_{2}

We prove an orbifold conjecture for conformal field theory with a solvable automorphism group. Namely, we show that if V is a

{C_2} -Cofiniteness of Cyclic-Orbifold Models

{C_2}

A modular invariance on the theta functions defined on vertex operator algebras

C2 -cofinite simple vertex operator algebra and G is a finite solvable automorphism group of V, then the fixed point vertex operator subalgebra

Vertex operator algebras generated by two conformal vectors whose τ-involutions generate S3

{V^G}

A new construction of the moonshine vertex operator algebra over the real number field

VG is also