Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory

Abstract

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.

87 pages, LaTex, New Appendix C and references added, minor corrections

References in corpus (7)

• Vertex Algebras and Algebraic Curves
• Affine orbifolds and rational conformal field theory extensions of W_{1+infinity}
• Rationality of conformally invariant local correlation functions on compactified Minkowski space
• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• On hot bangs and the arrow of time in relativistic quantum field theory
• Globally conformal invariant gauge field theory with rational correlation functions
• Conformal invariance and rationality in an even dimensional quantum field theory

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• The power of AQFT: the area law for entropy of localized quantum matter
• p-Adic and Adelic Rational Dynamical Systems
• Bloch waves and Non-commutative Tori of Magnetic Translations