Topological strings and their physical applications

Abstract

We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings, such as the notions of Calabi-Yau manifold and toric geometry, as well as physical methods developed for solving them, such as mirror symmetry, large N dualities, the topological vertex and quantum foam. In addition, we discuss applications of topological strings to N=1,2 supersymmetric gauge theories in 4 dimensions as well as to BPS black hole entropy in 4 and 5 dimensions. (These are notes from lectures given by the second author at the 2004 Simons Workshop in Mathematics and Physics.)

82 pages, 20 figures, LaTeX; v2: small corrections, added brief discussion of topological M-theory

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Cited by in corpus (17)

• Open string amplitudes and large order behavior in topological string theory
• General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation
• Direct Integration of the Topological String
• Refined Topological Vertex and Instanton Counting
• M-theory and a Topological String Duality
• A mini-course on topological strings
• Topological Open String Amplitudes On Orientifolds
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Lectures on Mirror Symmetry and Topological String Theory
• From effective actions to the background geometry
• The Ricci Curvature of Half-flat Manifolds
• Geometric Transitions on non-Kaehler Manifolds
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Metastring Theory and Modular Space-time
• On Minimal N=4 Topological Strings And The (1,k) Minimal Bosonic String
• Topological strings live on attractive manifolds