On the Geometry of the String Landscape and the Swampland

Abstract

We make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape. In particular we conjecture that such moduli are always given by expectation value of scalar fields and that moduli spaces with finite non-zero diameter belong to the swampland. We also conjecture that points at infinity in a moduli space correspond to points where an infinite tower of massless states appear, and that near these regions the moduli space is negatively curved. We also propose that there is no non-trivial 1-cycle of minimum length in the moduli space. This leads in particular to the prediction of the existence of a radially massive partner to the axion. These conjectures put strong constraints on inflaton potentials that can appear in a consistent quantum theory of gravity. Our conjectures are supported by a number of highly non-trivial examples from string theory. Moreover it is shown that these conditions can be violated if gravity is decoupled.

18 pages

References in corpus (3)

• The String Landscape and the Swampland
• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• Finiteness of volume of moduli spaces

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• The dark dimension, proton decay, and the length of the M-theory interval
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• On the incompleteness of $G_2$-moduli spaces along degenerating families of $G_2$-manifolds
• Warm inflation in Weyl geometric gravity
• Kiselev Black Holes in Anti-de Sitter Spacetime Are Not Viable
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Landscape of Narain CFTs
• Quintessence and false vacuum: Two sides of the same coin?
• Big-Bang Nucleosynthesis on a bubble universe nucleated in Kerr-AdS${}_5$ Black Hole
• At the End of the World: Local Dynamical Cobordism
• Bounds on tower mass scales in the presence of throats of different warping
• Cosmic Censorship of Trans-Planckian Field Ranges in Gravitational Collapse
• The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed of Primordial Black Holes
• Swampland conjectures for type IIB orientifolds with closed-string U(1)s
• Hořava-Lifshitz $F(\bar{R})$ theories and the Swampland
• cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
• Cosmic acceleration from string induced Galileons
• Moduli Stabilization in Stringy ISS Models
• Scale-dependence in DHOST inflation
• Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory
• Electroweak Quintessence Axion as Dark Energy
• Comments on Brane Recombination, Finite Flux Vacua, and the Swampland
• Infrared behavior in tame hyperbolizable two-field models
• Gauging the complex SYK model
• Aspects of 4d supersymmetric dynamics and geometry
• Swampland Conjectures and Cosmological Expansion
• The Cosmological Constant, Dark Matter and the ElectroWeak Scale meet in the Swampland
• Dynamical Tadpoles and Weak Gravity Constraints
• Holography as an Information Principle in Quantum Gravity
• A T-Fold Black Hole in Doubled Type IIB
• Species scale associated with Weinberg operator and bound on Majorana neutrino mass
• Solar System and Atomic Clock Bounds on Locally Coupled Swampland Scalars
• Constraining Spatial Curvature with Priors from Swampland Conjectures
• Breaking Free from the Swampland of Impossible Universes through the DESI Portal
• Towards an explicit model of large field inflation
• String Theory from Maximal Supersymmetry
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape
• Background instability of quintessence model in light of entropy and distance conjecture
• Toroidal $\&$ orbifold compactifications at large D and D-duality
• Thermodynamic Split Conjecture and an Observational Test for Cosmological Entropy
• Towards a String Realization of the Dark Dimension via T-folds
• Kination cosmology from scalar fields and gravitational-wave signatures
• String loop origin for dark radiation and superheavy dark matter in type IIB compactifications
• Dynamical-System analysis of single-axion monodromy inflation with periodically-modulated potentials
• A unique coupling of the massive spin-2 field to supergravity
• Systematic exploration of the non-geometric flux landscape
• Exact Geometries from Boundary Gravity
• On the Occurrence of Finite-time Singularities in Swampland-related Quintessence Dark Energy Models
• $E_9$ symmetry in the Heterotic String on $S^1$ and the Weak Gravity Conjecture