Topological strings and their physical applications

TL;DR

This paper provides an introductory review of topological strings, covering mathematical foundations and physical methods, and explores their applications to supersymmetric gauge theories and black hole entropy.

Contribution

It offers a comprehensive overview of topological string theory, integrating mathematical background with physical techniques and applications to gauge theories and black holes.

Findings

Develops mathematical background including Calabi-Yau and toric geometry.

Describes physical methods like mirror symmetry and topological vertex.

Discusses applications to supersymmetric gauge theories and black hole entropy.

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.)