Chern-Simons Theory, Matrix Models, and Topological Strings
Series: International Series of Monographs on Physics; 131;
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Product details:
- Publisher OUP Oxford
- Date of Publication 21 May 2015
- ISBN 9780198726333
- Binding Paperback
- No. of pages224 pages
- Size 236x160x10 mm
- Weight 378 g
- Language English
- Illustrations Numerous line drawings 0
Categories
Short description:
This book provides an introduction to some of the most recent developments in string theory, and in particular to their mathematical implications and their impact in knot theory and algebraic geometry.
MoreLong description:
In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.
... very carefully written ... will inspire a wide range of physicists and mathematicians for a long period of time.
Table of Contents:
Part I: Matrix Models, Chern-Simons Theory, and the Large N Expansion
Matrix models
Chern-Simons theory and knot invariants
Part II: Topological Strings
Topological sigma models
Topological strings
Calabi-Yau geometries
Part III: The Topological String / Gauge Theory Correspondence
String theory and gauge theory
String field theory and gauge theories
Geometric transitions
The topological vertex
Applications of the topological string / gauge theory correspondence
Symmetric polynomials
