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Instanton counting, quantum geometry...

Kimura, Taro.

Instanton counting, quantum geometry and algebra

Record Type:	Electronic resources : Monograph/item
Title/Author:	Instanton counting, quantum geometry and algebraby Taro Kimura.
Author:	Kimura, Taro.
Published:	Cham :Springer International Publishing :2021.
Description:	xxiii, 285 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Instantons.
Online resource:	https://doi.org/10.1007/978-3-030-76190-5
ISBN:	9783030761905$q(electronic bk.)

Instanton counting, quantum geometry and algebra
Kimura, Taro.

Instanton counting, quantum geometry and algebra[electronic resource] /by Taro Kimura. - Cham :Springer International Publishing :2021. - xxiii, 285 p. :ill., digital ;24 cm. - Mathematical physics studies,0921-3767. - Mathematical physics studies..

Instanton Counting and Localization -- Quiver Gauge Theory -- Supergroup Gauge Theory -- Seiberg-Witten Geometry -- Quantization of Geometry -- Operator Formalism of Gauge Theory -- Quiver W-Algebra -- Quiver Elliptic W-algebra.

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.

ISBN: 9783030761905$q(electronic bk.)

Standard No.: 10.1007/978-3-030-76190-5doiSubjects--Topical Terms:

898375
Instantons.

LC Class. No.: QC793.3.F5

Dewey Class. No.: 530.14

Instanton counting, quantum geometry and algebra
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300 $a xxiii, 285 p. : $b ill., digital ; $c 24 cm.
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520 $a 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.
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