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＜E-Book＞
Partition Functions and Automorphic Forms / edited by Valery A. Gritsenko, Vyacheslav P. Spiridonov
(Moscow Lectures. ISSN:25220322 ; 5)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2020
Language	English
Size	XIII, 415 p. 31 illus., 11 illus. in color : online resource
Authors	Gritsenko, Valery A editor Spiridonov, Vyacheslav P editor SpringerLink (Online service)
Subjects	LCSH:Mathematical physics LCSH:Elementary particles (Physics) LCSH:Quantum field theory LCSH:Special functions FREE:Mathematical Physics FREE:Mathematical Methods in Physics FREE:Elementary Particles, Quantum Field Theory FREE:Special Functions
Notes	A short introduction to the algebra, geometry, number theory and physics of moonshine -- Modified elliptic genus -- Superconformal indices and instanton partition functions -- On spinorial representations of involutory subalgebras of Kac-Moody algebras -- BPS spectra and invariants for three- and four-manifolds -- Introduction to the theory of elliptic hypergeometric integrals -- Feynman integrals and mirror symmetry -- Theory and applications of the elliptic Painlevé equation This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,…,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry HTTP:URL=https://doi.org/10.1007/978-3-030-42400-8

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