Chern-Simons Theory, Matrix Models, and Topological Strings

Paperback | June 21, 2015

byMarcos Marino

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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 thiscorrespondence 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 geometryand 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 thisduality 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.

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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 thiscorrespondence relates Chern-Simons theory, a topologica...

Marcos Marino is Full Professor in the Department of Mathematics at the University of Geneva.

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Format:PaperbackDimensions:224 pagesPublished:June 21, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198726333

ISBN - 13:9780198726333

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Table of Contents

Part I: Matrix Models, Chern-Simons Theory, and the Large N Expansion1. Matrix models2. Chern-Simons theory and knot invariantsPart II: Topological Strings3. Topological sigma models4. Topological strings5. Calabi-Yau geometriesPart III: The Topological String / Gauge Theory Correspondence6. String theory and gauge theory7. String field theory and gauge theories8. Geometric transitions9. The topological vertex10. Applications of the topological string / gauge theory correspondenceA. Symmetric polynomials

Editorial Reviews

"The book gives a good overview of the developments in the field, in which its author has himself played an important role. The book shows nicely how the different ideas are related, and how they can be combined to allow one to do very explicit calculations." --Marcel L. Vonk, Mathematical Reviews