Seiberg Witten Theory And Integrable Systems
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Seiberg Witten Theory And Integrable Systems
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Author : Andrei Marshakov
language : en
Publisher: World Scientific
Release Date : 1999
Seiberg Witten Theory And Integrable Systems written by Andrei Marshakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
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.
Seiberg Witten Theory And The Integrable Systems
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Author : Andrei Marshakov
language : en
Publisher: World Scientific
Release Date : 1999-03-26
Seiberg Witten Theory And The Integrable Systems written by Andrei Marshakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-26 with Science categories.
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.
Symmetries Integrable Systems And Representations
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Author : Kenji Iohara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries Integrable Systems And Representations written by Kenji Iohara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Integrable Hierarchies And Modern Physical Theories
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Author : Henrik Aratyn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Hierarchies And Modern Physical Theories written by Henrik Aratyn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Proceedings of the NATO Advanced Research Workshop, Chicago, USA, July 22-26, 2000
Instanton Counting Quantum Geometry And Algebra
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Author : Taro Kimura
language : en
Publisher: Springer Nature
Release Date : 2021-07-05
Instanton Counting Quantum Geometry And Algebra written by Taro Kimura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Science categories.
This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.
Notes On Seiberg Witten Theory
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Author : Liviu I. Nicolaescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Notes On Seiberg Witten Theory written by Liviu I. Nicolaescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations and the group of gauge transformations, then look at algebraic surfaces. A final chapter presents in great detail a cut-and-paste technique for computing Seiberg-Witten invariants, covering elliptic equations on manifolds with cylindrical ends, finite energy monopoles on cylindrical manifolds, local and global properties of the moduli spaces of finite energy monopoles, and the process of reconstructing the space of monopoles on a 4-manifold decomposed into several parts by a hypersurface. Annotation copyrighted by Book News, Inc., Portland, OR.
From Hodge Theory To Integrability And Tqft
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Author : Ron Donagi
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
From Hodge Theory To Integrability And Tqft written by Ron Donagi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*-geometry (tt* stands for topological-antitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*-geometry has become a fast moving and exciting research area. This book, loosely based on the 2007 Augsburg, Germany workshop "From tQFT to tt* and Integrability", is the perfect introduction to the range of mathematical topics relevant to tt*-geometry. It begins with several surveys of the main features of tt*-geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and non-commutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics. With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it."--Publisher's website.
Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory
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Author : S. Pakuliak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory written by S. Pakuliak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.
Supersymmetry And Unification Of Fundamental Interactions Proceedings Of The Ix International Conference Susy 01
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Author : A V Gladyshev
language : en
Publisher: World Scientific
Release Date : 2002-03-28
Supersymmetry And Unification Of Fundamental Interactions Proceedings Of The Ix International Conference Susy 01 written by A V Gladyshev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-28 with Science categories.
This book addresses the theoretical, phenomenological and experimental aspects of supersymmetry in particle physics as well as its implications in cosmology.
Integrability Quantization And Geometry I Integrable Systems
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Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12
Integrability Quantization And Geometry I Integrable Systems written by Sergey Novikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-12 with Education categories.
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.