2004/12/13 by Nikolay Nikolov, Nikolay M. Nikolov, Nikolov, Nikolay M. +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0412039
87 pages, LaTex, New Appendix C and references added, minor corrections
openalex publication_date 2004/12/13 · arxiv created 2005/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field theory. Many features, believed to be peculiar to chiral 2D (= two dimensional) CFT, are shown to have a counterpart in any (even dimensional) globally conformal invariant quantum field theory. The treatment is based on a recently introduced higher dimensional extension of the concept of vertex algebra.