Instanton Counting, Quantum Geometry and Algebra (Mathematical Physics Studies)

This book provides a comprehensive overview of recent developments in gauge theory, particularly four-dimensional N = 2 supersymmetric gauge theory, and its connections to various fields in mathematics, including algebraic geometry, geometric representation theory, and vertex operator algebras.

The author presents a systematic description of the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions, and explains how to integrate out the instanton moduli space using an equivariant localization formula.

The book also covers the Seiberg–Witten theory, a geometric description of supersymmetric gauge theory, and the quantum algebraic structure of supersymmetric gauge theory.

The author introduces the free field realization of gauge theory and discusses the underlying infinite-dimensional algebraic structure, highlighting the connection with representation theory of quivers.

The book provides a detailed explanation of how the gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

This comprehensive guide is essential for researchers and students interested in gauge theory and its connections to mathematics, providing a solid foundation for understanding recent developments in the field.