2003/03/05 by Yi-Zhi Huang, Huang, Yi-Zhi · 3 citations
Mathematics · Physics and Astronomy · #17B69 #32N10 #34M35 #81T40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA #msc:17B69 #msc:32N10 #msc:34M35 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/0303049
71 pages
openalex publication_date 2003/03/05 · arxiv created 2004/08/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) the weight of any nonzero homogeneous elements of V is nonnegative and the weight zero subspace is one-dimensional, (ii) every N-gradable weak V-module is completely reducible and (iii) V is C2-cofinite. We establish the fundamental properties of these functions, including suitably formulated commutativity, associativity and modular invariance. The method we develop and use here is completely different from the one previously used by Zhu and other people. In particular, we show that the q-traces of products of certain geometrically-modified intertwining operators satisfy modular invariant systems of differential equations which, for any fixed modular parameter, reduce to doubly-periodic systems with only regular singular points. Together with the results obtained by the author in the genus-zero case, the results of the present paper solves essentially the problem of constructing chiral genus-one weakly conformal field theories from the representations of a vertex operator algebra satisfying the conditions above.