Mathematical Physics Studies
cover

Instanton Counting, Quantum Geometry and Algebra

Authors: Kimura, Taro

  • Focuses on algebraic aspects of supersymmetric gauge theories
  • Discusses geometrical and algebraic aspects of Nekrasov instanton calculus and some interesting generalizations of those calculus
  • Consists of three parts, instanton calculus, quantum geometry, and quantum algebra, with a lot of background information with clear technical exposition
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eBook $109.00
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  • The eBook version of this title will be available soon
  • Due: September 1, 2021
  • ISBN 978-3-030-76190-5
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Hardcover $149.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: August 4, 2021
  • ISBN 978-3-030-76189-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
About this book

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.

About the authors

Professor Taro Kimura is Maître de Conérences (Assistant Professor) working at Mathematical Physics group of Institut de Mathématiques de Bourgogne, Université Bourgogne Franche-Comté (UBFC), France. Before moving to UBFC, he has been Postdoctoral Researcher at RIKEN, CEA Saclay, then Research Associate, Junior Faculty Member, at Keio University. He obtained his Ph.D. degree in Theoretical/Mathematical Physics at the University of Tokyo in 2012 and then obtained the habilitation in 2020 at UBFC.

His research interest lies in theoretical physics/mathematical physics. In particular,  he is mainly exploring quantum field theory, and its mathematical aspects and applications.


Buy this book

eBook $109.00
price for USA in USD
  • The eBook version of this title will be available soon
  • Due: September 1, 2021
  • ISBN 978-3-030-76190-5
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $149.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: August 4, 2021
  • ISBN 978-3-030-76189-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
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Bibliographic Information

Bibliographic Information
Book Title
Instanton Counting, Quantum Geometry and Algebra
Authors
Series Title
Mathematical Physics Studies
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-76190-5
DOI
10.1007/978-3-030-76190-5
Hardcover ISBN
978-3-030-76189-9
Series ISSN
0921-3767
Edition Number
1
Number of Pages
X, 290
Number of Illustrations
30 b/w illustrations
Topics