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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
101/2006

Modular invariance for conformal full field algebras

Yi-Zhi Huang and Liang Kong

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 (Y.-Z. Huang and L. Kong, Full field algebras, to appear; math.QA/0511328), we prove that all these functions are modular invariant.

Received:
Sep 22, 2006
Published:
Sep 22, 2006

Related publications

inJournal
2010 Repository Open Access
Yi-Zhi Huang and Liang Kong

Modular invariance for conformal full field algebras

In: Transactions of the American Mathematical Society, 362 (2010) 6, pp. 3027-3067