Modular invariance of vertex operator algebras satisfying $C_{2}$-cofiniteness
Modular invariance of vertex operator algebras satisfying $C_{2}$-cofiniteness
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DOI：
10.1215/s0012-7094-04-12212-2
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发表时间：
2002-09
影响因子：
2.5
通讯作者：
M. Miyamoto
中科院分区：
文献类型：
--
作者：
M. Miyamoto
我们证明，C_2-余有限性足以证明顶点算子代数的模不变性，而无需假设朱代数的半简单性。例如，如果 VOA V=\oplus_{m=0}^{\infty}V_m 是 C_2-余有限，则 V 模块的广义字符所跨越的空间在 SL_2(\Z) 的作用下是不变的。在这种情况下，中心电荷和共形权重都是有理数。即满足C_2余有限性的VOA在某种意义上是有理共形场论。我们还表明，C_2-余有限性相当于每个弱模块都是\N级弱模块的条件，它是L(0)的广义特征空间的直和。
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).