Lectures on Mirror Symmetry and Topological String Theory

TL;DR

This paper provides an overview of mirror symmetry and topological string theory, highlighting their mathematical structures, physical implications, and computational techniques for higher genus amplitudes.

Contribution

It reviews the construction of topological string theories, the role of mirror symmetry, and recursive methods for computing higher genus amplitudes, connecting physics and mathematics.

Findings

Mirror symmetry links A- and B-models with surprising mathematical connections.

Topological string amplitudes can be computed recursively as polynomials.

Coupling topological strings to gravity yields insights into quantum geometry.

Abstract

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observables are only the elements of the chiral ring. When coupled to gravity, this leads to topological string theory. The identification of the topological string A- and B-models by mirror symmetry leads to surprising connections in mathematics and provides tools for exact computations as well as new insights in physics. A recursive construction of the higher genus amplitudes of topological string theory expressed as polynomials is reviewed.