Modular invariance for conformal full field algebras
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- by Yi-Zhi Huang and Liang Kong PDF
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Abstract:
Let $V^{L}$ and $V^{R}$ be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let $F$ be a conformal full field algebra over $V^{L}\otimes V^{R}$. We prove that the $q_{\tau }$-$\overline {q_{\tau }}$-traces (natural traces involving $q_{\tau }=e^{2\pi i\tau }$ and $\overline {q_{\tau }}= \overline {e^{2\pi i\tau }}$) of geometrically modified genus-zero correlation functions for $F$ are convergent in suitable regions and can be extended to doubly periodic functions with periods $1$ and $\tau$. We obtain necessary and sufficient conditions for these functions to be modular invariant. In the case that $V^{L}=V^{R}$ and $F$ is one of those constructed by the authors in an earlier paper, we prove that all these functions are modular invariant.References
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Additional Information
- Yi-Zhi Huang
- Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019
- MR Author ID: 239657
- ORCID: 0000-0002-6121-2539
- Email: yzhuang@math.rutgers.edu
- Liang Kong
- Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103, Leipzig, Germany – and – Institut Des Hautes Études Scientifiques, Le Bois-Marie, 35, Route De Chartres, F-91440 Bures-sur-Yvette, France
- Address at time of publication: Institute for Advanced Study, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: kong.fan.liang@gmail.com
- Received by editor(s): March 10, 2008
- Published electronically: December 22, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 3027-3067
- MSC (2000): Primary 17B69; Secondary 81T40
- DOI: https://doi.org/10.1090/S0002-9947-09-04933-2
- MathSciNet review: 2592945