Seiberg-Witten Theory and the Integrable Systems

By: Andrei Marshakov

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Hardcover | 1 December 1997

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Hardcover
260 Pages

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22.86 x 16.51 x 1.91

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Published: 1st December 1997

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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 l-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 axe 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.

Industry Reviews

"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

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Science in General Maths for Scientists Booktopia Publisher Services World Scientific Publishing

Introduction	p. 4
SUSY Yang-Mille theories	p. 9
Integrable systems	p. 26
Integrable equations in 2D topological string theories	p. 52
The Seiberg-Witten anzatz	p. 71
Generating differential and Whitham hierarchy	p. 105
Prepotential of the Seiberg-Witten Theory	p. 144
Seiberg-Witten theory from strings	p. 182
Conclusion	p. 204
Riemann surfaces and Theta-functions	p. 206
KP hierarchy and theory of free fermions	p. 216
Residue formula for the N=2 Calogero-Moser system	p. 222
Algebra of differentials for the Calogero-Moser system	p. 226
Explicit derivation in elliptic case	p. 233
Table of Contents provided by Blackwell. All Rights Reserved.

Seiberg-Witten Theory and the Integrable Systems

At a Glance

New Edition

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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