Calabi-Yau metrics and string compactification

TL;DR

This paper reviews methods for approximating Calabi-Yau metrics, which are essential for string compactification, highlighting their role in deriving physical predictions despite the lack of explicit solutions.

Contribution

It surveys numerical and analytical approaches to approximate Calabi-Yau metrics and discusses their application in superstring theory predictions.

Findings

Various approximation techniques for Calabi-Yau metrics are effective.

Approximate metrics enable physical predictions in string theory.

The survey connects mathematical methods with physical applications.

Abstract

Yau proved an existence theorem for Ricci-flat K\"ahler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.