Modular-invariance of trace functions in orbifold theory and generalized moonshine

被引:283
作者
Dong, CY [1 ]
Li, HS
Mason, G
机构
[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA
[2] Rutgers State Univ, Dept Math Sci, Camden, NJ 08102 USA
基金
美国国家科学基金会;
关键词
D O I
10.1007/s002200000242
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of the theory of rational orbifold models in conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a certain finiteness condition on a rational Vertex operator algebra V which holds in all known examples, we determine the precise number of g-twisted sectors for any automorphism g of V of finite order. We prove that the trace functions and correlation functions associated with such twisted sectors are holomorphic functions in the upper half-plane and, under suitable conditions, afford a representation of the modular group of the type prescribed in string theory. We establish the rationality of conformal weights and central charge. In addition to conformal field theory itself, where our conclusions are required on physical grounds, there are applications to the generalized Moonshine conjectures of Conway-Norton-Queen and to equivariant elliptic cohomology.
引用
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页码:1 / 56
页数:56
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