Lectures on the Swampland Program in String Compactifications

TL;DR

The paper introduces the Swampland program as a framework to distinguish EFTs that can be UV completed within quantum gravity from those that cannot, using string theory as a testbed. It presents the core conjectures—No Global Symmetries, Completeness, Weak Gravity, Swampland Distance, Emergence, AdS/non-SUSY AdS Instability, and de Sitter—along with motivations, evidence from string compactifications, and interrelations (e.g., WGC with SDC and Emergence). The notes emphasize how these conjectures constrain low-energy physics, inflation, and cosmology, and discuss strong versions and open questions, highlighting a coherent, interconnected structure that governs quantum gravity consistency. The discussed connections suggest a roadmap toward understanding why certain IR phenomena (like approximate symmetries, light towers, and field-range limitations) arise from UV quantum gravity principles and dualities in string theory.

Abstract

The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland conjectures. In these lecture notes, we provide a pedagogical introduction to the most important Swampland conjectures, their connections and their realization in string theory compactifications. The notes are based on the series of lectures given by Irene Valenzuela at the online QFT and Geometry summer school in July 2020.

Figures (27)

• Figure 1: Each EFT has an energy cut-off up to which the description is valid. Typical reference scales in high energy physics are indicated here, including the cosmological constant, QCD, electroweak symmetry breaking, and the Planck scale $M_p$. Also indicated is a possible estimation of the Hubble scale $H$ for inflation, the compactification scale $M_{KK}$ and the string scale $M_s$, at which stringy effects become important.
• Figure 2: The Swampland and Landscape of EFTs. The space of consistent EFTs forms a cone because Swampland constraints become stronger at high energies.
• Figure 3: The Swampland and Landscape of EFTs. Cross section of figure \ref{['fig:cone']}. The effective field theory (EFT$_0$) is in the landscape/swampland if it is used to describe a process of characteristic energy $E_1/E_2$.
• Figure 4: Map of the Swampland conjectures. The conjectures in black are at the core of the Swampland program, and we will discuss them in detail in the following. The conjectures in purple will also be discussed throughout the lectures, but sometimes in less detail.
• Figure 5: Road map of the Swampland program.