Chern-Simons Theory, Matrix Models, and Topological Strings

Hardcover | September 15, 2005

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 themathematical 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.

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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, Department of Theoretical Physics, CERN, Geneva, Switzerland and Department of Mathematics, Instituto Superior Tecnico, Lisboa, Portugal

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Kobo ebook|Sep 3 2015

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Format:HardcoverDimensions:216 pages, 9.21 × 6.14 × 0.66 inPublished:September 15, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198568495

ISBN - 13:9780198568490

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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

`... very carefully written ..., will inspire a wide range of physicists and mathematicians for a long period of time.'Albrecht Klemm, University of Wisconsin