Téléchargez le livre : Instanton Counting, Quantum Geometry and Algebra

Instanton Counting, Quantum Geometry and Algebra

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Éditeur :

Springer


Collection :

Mathematical Physics Studies

Paru le : 2021-07-05

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Description

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 O-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.
Pages
285 pages
Collection
Mathematical Physics Studies
Parution
2021-07-05
Marque
Springer
EAN papier
9783030761899
EAN PDF
9783030761905
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
28
Taille du fichier
4495 Ko
Prix
137,14 €
EAN EPUB
9783030761905
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
28
Taille du fichier
19763 Ko
Prix
137,14 €

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