Modular invariance of vertex operator algebras satisfying C_2-cofiniteness

Details Modular invariance of vertex operator algebras satisfying C_2-cofiniteness Modular invariance of vertex operator algebras satisfying C_2-cofiniteness

2002-09-10

arxiv.org/abs/math/0209101v2

Mathematics

Quantum Algebra

34 pages. We get rid of the condition of being of``CFT type''. Latex

Scientific paper

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).

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