Communications in Mathematical Physics

, Volume 214, Issue 1, pp 1–56 | Cite as

Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine

  • Chongying Dong
  • Haisheng Li
  • Geoffrey Mason

Abstract:

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Chongying Dong
    • 1
  • Haisheng Li
    • 2
  • Geoffrey Mason
    • 1
  1. 1.Department of Mathematics, University of California, Santa Cruz, CA 95064, USAUS
  2. 2.Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USAUS

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