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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Instanton Counting, Quantum Geometry and Algebra (Paperback, 1st ed. 2021)
Loot Price: R4,108
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Instanton Counting, Quantum Geometry and Algebra (Paperback, 1st ed. 2021)
Series: Mathematical Physics Studies
Expected to ship within 10 - 15 working days
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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 -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.
General
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