Topological strings and their physical applications

TLDR: In this article, the authors give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories, including the notions of Calabi-Yau manifold and toric geometry, as well as physical methods developed for solving them.

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.)