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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 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.
List of contents
- Part I: Matrix Models, Chern-Simons Theory, and the Large N Expansion
- 1: Matrix models
- 2: Chern-Simons theory and knot invariants
- Part II: Topological Strings
- 3: Topological sigma models
- 4: Topological strings
- 5: Calabi-Yau geometries
- Part III: The Topological String / Gauge Theory Correspondence
- 6: String theory and gauge theory
- 7: String field theory and gauge theories
- 8: Geometric transitions
- 9: The topological vertex
- 10: Applications of the topological string / gauge theory correspondence
- A: Symmetric polynomials
About the author
Marcos Marino,
Full Professor, Department of Mathematics, University of Geneva
Summary
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.
Additional text
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.
Report
... very carefully written ... will inspire a wide range of physicists and mathematicians for a long period of time. Albrecht Klemm, University of Wisconsin
