Modular invariance for conformal full field algebras
Yi-Zhi Huang and Liang Kong
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Submission date: 22. Sep. 2006
published in: Transactions of the American Mathematical Society, 362 (2010) 6, p. 3027-3067
DOI number (of the published article): 10.1090/S0002-9947-09-04933-2
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Let and 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 . We prove that the --traces (natural traces involving and ) 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 . We obtain necessary and sufficient conditions for these functions to be modular invariant. In the case that and F is one of those constructed by the authors in (Y.-Z. Huang and L. Kong, Full field algebras, to appear; math.QA/0511328), we prove that all these functions are modular invariant.