Lectures on Mirror Symmetry

TL;DR

This paper introduces mirror symmetry in string theory on Calabi-Yau manifolds, focusing on computational tools like toric geometry and Picard-Fuchs equations, with illustrative examples.

Contribution

It provides an accessible introduction to mirror symmetry concepts and techniques, emphasizing applications in calculating physical quantities like Yukawa couplings.

Findings

Demonstrates construction of mirror pairs

Shows how to compute Yukawa couplings

Illustrates methods with a non-trivial example

Abstract

We give an introduction to mirror symmetry of strings on Calabi-Yau manifolds with an emphasis on its applications e.g. for the computation of Yukawa couplings. We introduce all necessary concepts and tools such as the basics of toric geometry, resolution of singularities, construction of mirror pairs, Picard-Fuchs equations, etc. and illustrate all of this on a non-trivial example. Extended version of a lecture given at the Third Baltic Student Seminar, Helsinki September 1993