Beginners lectures on flux compactifications and related Swampland topics

TL;DR

This paper provides an accessible introduction to flux compactifications in string theory, emphasizing recent Swampland conjectures that challenge the existence of certain stable vacua, with minimal technical prerequisites.

Contribution

It offers a pedagogical overview of flux compactifications and discusses recent Swampland developments questioning the viability of AdS and dS vacua without heavy reliance on supersymmetric geometry.

Findings

Swampland conjectures suggest constraints on stable vacua.

Recent arguments challenge the existence of small extra dimension AdS vacua.

The status of dS vacua remains uncertain due to theoretical tensions.

Abstract

These lecture notes provide a pedagogical introduction, with exercises, to the techniques used in attempts to construct vacua with stabilised moduli in string theory. The reader is only assumed to have a basic knowledge of general relativity, geometry and field theory. We emphasize physical arguments and focus on the latest developments involving the Swampland program that point to a tension for the existence of AdS vacua with small extra dimensions or dS vacua with parametric control. We include a brief summary of the current status of these thorny issues. Unlike many other reviews we make almost no use of the technicalities associated to supersymmetric geometries. These notes are largely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge Theory and in the Tehran School on Swampland Program held in the summer of 2022.