Chern-Simons Theory, Matrix Models, and Topological Strings

Erscheinungsjahr 2005
ISBN: 978-0-19-856849-0
Verlag: OUP Oxford

Buch, Englisch, 212 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 487 g

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.

Autoren/Hrsg.

Marino, Marcos

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Naturwissenschaften Physik Physik Allgemein
• Naturwissenschaften Physik Quantenphysik Radioaktivität
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Naturwissenschaften Physik Quantenphysik Hochenergiephysik
• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

- 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

Über Autor(innen)

Marcos Marino, Department of Theoretical Physics, CERN, Geneva, Switzerland and Department of Mathematics, Instituto Superior Técnico, Lisboa, Portugal