The Geometer's Toolkit to String Compactifications

TL;DR

This paper provides an introduction to geometric methods, especially toric geometry, used in string theory compactifications, focusing on the mathematical techniques rather than physical implications.

Contribution

It offers a comprehensive overview of geometric constructions like toric geometry and their application to string theory compactifications, emphasizing the mathematical perspective.

Findings

Detailed explanation of toroidal orbifolds and their desingularization

Techniques for constructing and analyzing orientifold quotients

Application of toric geometry methods to string compactifications

Abstract

These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is wholly on the geometry side, not on the physics. The treated topics include toroidal orbifolds, methods of toric geometry, desinglularization of toroidal orbifolds and their orientifold quotients.