Seiberg-Witten Theory and Integrable Systems ペーパーバック – 1999/6/1

英語版 Andrei Marshakov (著)

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In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical physics -- systems of integrable nonlinear differential equations and their algebro-geometric solutions.First, the book reviews what is known about the physical problem: the construction of low-energy effective actions for the N=2 Yang-Mills theories from the traditional viewpoint of quantum field theory. Then the necessary background information from the theory of integrable systems is presented. In particular the author considers the definition of the algebro-geometric solutions to integrable systems in terms of complex curves or Riemann surfaces and the generating meromorphic 1-form. These definitions are illustrated in detail on the basic example of the periodic Toda chain.Several "toy-model" examples of string theory solutions where the structures of integrable systems appear are briefly discussed. Then the author proceeds to the Seiberg-Witten solutions and show that they are indeed defined by the same data as finite-gap solutions to integrable systems. The complete formulation requires the introduction of certain deformations of the finite-gap solutions described in terms of quasiclassical or Whitham hierarchies. The explicit differential equations and direct computations of the prepotential of the effective theory are presented and compared when possible with the well-known computations from supersymmetric quantum gauge theories.Finally, the book discusses the properties of the exact solutions to SUSY Yang-Mills theories and their relation to integrable systems in the general context of the modern approach to nonperturbative string or M-theory.

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本の長さ

200ページ
言語

英語
出版社

World Scientific Pub Co Inc
発売日

1999/6/1
寸法

15.24 x 1.52 x 21.34 cm
ISBN-10

9810236379
ISBN-13

978-9810236373
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商品の説明

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"This book provides a broad survey of some of the pioneering developments in quantum field theory and string theory. It is accessible to advanced students in mathematics and theoretical physics, and enjoyable to experienced researchers with background in quantum field theory, string theory and integrable systems." Mathematical Reviews, 2001

登録情報

出版社 ‏ : ‎ World Scientific Pub Co Inc (1999/6/1)
発売日 ‏ : ‎ 1999/6/1
言語 ‏ : ‎ 英語
ペーパーバック ‏ : ‎ 200ページ
ISBN-10 ‏ : ‎ 9810236379
ISBN-13 ‏ : ‎ 978-9810236373
寸法 ‏ : ‎ 15.24 x 1.52 x 21.34 cm

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Seiberg-Witten Theory and Integrable Systems ペーパーバック – 1999/6/1

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