Sharpening the Distance Conjecture in Diverse Dimensions

Abstract

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance $\Vert \varphi \Vert$ as $m\sim \exp (-\lambda \Vert \varphi \Vert )$, where $\lambda$ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of $\lambda$ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in $d$ dimensions: $\lambda \ge 1/\sqrt{d-2}$. In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in $d=\text{4 - 10}$ dimensions, and (3) it is saturated in many examples of minimal supergravity in $d=\text{4 - 10}$ dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with $\lambda <1/\sqrt{d-2}$ discussed previously in the literature are always accompanied by even lighter towers with $\lambda \ge 1/\sqrt{d-2}$, thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.

arXiv comment83 pages, 6 figures

References in corpus (69)

• Unity of Superstring Dualities
• The String Landscape, Black Holes and Gravity as the Weakest Force
• On the Geometry of the String Landscape and the Swampland
• Monodromy in the CMB: Gravity Waves and String Inflation
• Symmetries and Strings in Field Theory and Gravity
• Gravity Waves and Linear Inflation from Axion Monodromy
• Quintessence: A Review
• Cosmological Relaxation of the Electroweak Scale
• Inflationary Cosmology
• Black Holes and Large N Species Solution to the Hierarchy Problem
• U-duality and M-Theory
• Eternal inflation and its implications
• Infinite Distances in Field Space and Massless Towers of States
• Disturbing Implications of a Cosmological Constant
• Trans-Planckian Censorship and the Swampland
• The Trouble with de Sitter Space
• Black Hole Condensation and the Unification of String Vacua
• String Theory and Quintessence
• Tensionless Strings and the Weak Gravity Conjecture
• Naturalness and the Weak Gravity Conjecture
• Super-Planckian Spatial Field Variations and Quantum Gravity
• The Weak Gravity Conjecture and Scalar Fields
• Evidence for a Lattice Weak Gravity Conjecture
• Transplanckian axions !?
• Emergence and the Swampland Conjectures
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• BPS States of Exceptional Non-Critical Strings
• A Stringy Test of the Scalar Weak Gravity Conjecture
• The Weak Gravity Conjecture in three dimensions
• A Tower Weak Gravity Conjecture from Infrared Consistency
• Infinite Distance Networks in Field Space and Charge Orbits
• The Swampland Distance Conjecture for Kahler moduli
• Backreacted Axion Field Ranges in String Theory
• Natural Inflation and Quantum Gravity
• Planckian Axions and the Weak Gravity Conjecture
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• The web of swampland conjectures and the TCC bound
• Asymptotic Flux Compactifications and the Swampland
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Constraints on Axion Inflation from the Weak Gravity Conjecture
• Repulsive Forces and the Weak Gravity Conjecture
• Swampland Conjectures for Strings and Membranes
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
• The asymptotic dS Swampland Conjecture - a simplified derivation and a potential loophole
• Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds
• Photon Masses in the Landscape and the Swampland
• Cosmological solutions of supercritical string theory
• Conditions for (No) Eternal Inflation
• All Couplings of Minimal Six-dimensional Supergravity
• Dimensional Reduction and (Anti) de Sitter Bounds
• The FL bound and its phenomenological implications
• The Convex Hull Swampland Distance Conjecture and Bounds on Non-geodesics
• A Geometric Realization of Confinement
• Chiral Global Embedding of Fibre Inflation Models
• Transplanckian Censorship and Global Cosmic Strings
• Asymptotic Observables and the Swampland
• The Weak Gravity Conjecture and Axion Strings
• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Membrane Limits in Quantum Gravity
• Vacuum Structure and the Arrow of Time
• New solutions with accelerated expansion in string theory
• Abelian Vectors and Self-Dual Tensors in Six-Dimensional Supergravity
• Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold
• Black Holes, Moduli, and Long-Range Forces
• Eternal inflation and the present universe
• Infinite Distance and Zero Gauge Coupling in 5d Supergravity
• The Weak Gravity Conjecture and BPS Particles

Cited by in corpus (5)

• The Emergence Proposal in Quantum Gravity and the Species Scale
• Asymptotic Accelerated Expansion in String Theory and the Swampland
• (Quasi-) de Sitter solutions across dimensions and the TCC bound
• AdS scale separation and the distance conjecture
• Infinite distances in multicritical CFTs and higher-spin holography