Instanton Counting, Quantum Geometry and Algebra

Instanton Counting, Quantum Geometry and Algebra
Author :
Publisher : Springer Nature
Total Pages : 297
Release :
ISBN-10 : 9783030761905
ISBN-13 : 3030761908
Rating : 4/5 (05 Downloads)

Book Synopsis Instanton Counting, Quantum Geometry and Algebra by : Taro Kimura

Download or read book Instanton Counting, Quantum Geometry and Algebra written by Taro Kimura and published by Springer Nature. This book was released on 2021-07-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Instanton Counting, Quantum Geometry and Algebra Related Books

Instanton Counting, Quantum Geometry and Algebra
Language: en
Pages: 297
Authors: Taro Kimura
Categories: Science
Type: BOOK - Published: 2021-07-05 - Publisher: Springer Nature

DOWNLOAD EBOOK

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various
Lie Theory and Its Applications in Physics
Language: en
Pages: 526
Authors: Vladimir Dobrev
Categories: Mathematics
Type: BOOK - Published: 2023-01-29 - Publisher: Springer Nature

DOWNLOAD EBOOK

This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in P
The Theory and Applications of Instanton Calculations
Language: en
Pages: 325
Authors: Manu Paranjape
Categories: Science
Type: BOOK - Published: 2017-11-16 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This book explains in detail the key concepts, calculations and applications elucidating quantum tunnelling mediated by instantons, using the Feynman path integ
Topological Recursion and its Influence in Analysis, Geometry, and Topology
Language: en
Pages: 549
Authors: Chiu-Chu Melissa Liu
Categories: Topology
Type: BOOK - Published: 2018-11-19 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which
Elementary Introduction to Quantum Geometry
Language: en
Pages: 329
Authors: Jan Ambjorn
Categories: Science
Type: BOOK - Published: 2022-11-02 - Publisher: CRC Press

DOWNLOAD EBOOK

This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of