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Conformal Field Theory, Automorphic Forms and Related Topics

2014-08-22 Mathematics
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Release : 2014-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 313/5 ( reviews)

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Book Synopsis Conformal Field Theory, Automorphic Forms and Related Topics by : Winfried Kohnen

Download or read book Conformal Field Theory, Automorphic Forms and Related Topics written by Winfried Kohnen. This book was released on 2014-08-22. Available in PDF, EPUB and Kindle. Book excerpt: This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).

Conformal Field Theory with Gauge Symmetry

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 886/5 ( reviews)

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Book Synopsis Conformal Field Theory with Gauge Symmetry by : Kenji Ueno

Download or read book Conformal Field Theory with Gauge Symmetry written by Kenji Ueno. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.

Partition Functions and Automorphic Forms

2020-07-09 Mathematics
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Release : 2020-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 006/5 ( reviews)

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Book Synopsis Partition Functions and Automorphic Forms by : Valery A. Gritsenko

Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko. This book was released on 2020-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vertex Operator Algebras, Number Theory and Related Topics

2020-07-13 Education
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Release : 2020-07-13
Genre : Education
Kind : eBook
Book Rating : 382/5 ( reviews)

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Book Synopsis Vertex Operator Algebras, Number Theory and Related Topics by : Matthew Krauel

Download or read book Vertex Operator Algebras, Number Theory and Related Topics written by Matthew Krauel. This book was released on 2020-07-13. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

A Mathematical Introduction to Conformal Field Theory

2008-09-11 Science
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Release : 2008-09-11
Genre : Science
Kind : eBook
Book Rating : 282/5 ( reviews)

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Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher

Download or read book A Mathematical Introduction to Conformal Field Theory written by Martin Schottenloher. This book was released on 2008-09-11. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book gives a self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The second part surveys some more advanced topics of conformal field theory.

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