The Weak Gravity Conjecture and Axion Strings

Abstract

Strong (sublattice or tower) formulations of the Weak Gravity Conjecture (WGC) imply that, if a weakly coupled gauge theory exists, a tower of charged particles drives the theory to strong coupling at an ultraviolet scale well below the Planck scale. This tower can consist of low-spin states, as in Kaluza-Klein theory, or high-spin states, as with weakly-coupled strings. We provide a suggestive bottom-up argument based on the mild $p$-form WGC that, for any gauge theory coupled to a fundamental axion through a $\theta F\wedge F$ term, the tower is a stringy one. The charge-carrying string states at or below the WGC scale $g{M}_{\mathrm{Pl}}$ are simply axion strings for $\theta$, with charged modes arising from anomaly inflow. Kaluza-Klein theories evade this conclusion and postpone the appearance of high-spin states to higher energies because they lack a $\theta F\wedge F$ term. For abelian Kaluza-Klein theories, modified arguments based on additional abelian groups that interact with the Kaluza-Klein gauge group sometimes pinpoint a mass scale for charged strings. These arguments reinforce the Emergent String and Distant Axionic String Conjectures. We emphasize the unproven assumptions and weak points of the arguments, which provide interesting targets for further work. In particular, a sharp characterization of when gauge fields admit $\theta F\wedge F$ couplings and when they do not would be immensely useful for particle phenomenology and for clarifying the implications of the Weak Gravity Conjecture.

arXiv comment21 pages, v2: minor changes

References in corpus (55)

• 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
• Toward Realistic Intersecting D-Brane Models
• On Flux Quantization In M-Theory And The Effective Action
• Torsion-balance tests of the weak equivalence principle
• A Natural Framework for Chaotic Inflation
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Infinite Distances in Field Space and Massless Towers of States
• Tensionless Strings and the Weak Gravity Conjecture
• Naturalness and the Weak Gravity Conjecture
• Super-Planckian Spatial Field Variations and Quantum Gravity
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Evidence for a Lattice Weak Gravity Conjecture
• Unbroken B-L Symmetry
• Emergence and the Swampland Conjectures
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• 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
• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Repulsive Forces and the Weak Gravity Conjecture
• Swampland Conjectures for Strings and Membranes
• Modified instanton sum in QCD and higher-groups
• The Swampland Distance Conjecture and Towers of Tensionless Branes
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Photon Masses in the Landscape and the Swampland
• Instanton Corrections and Emergent Strings
• Three-Form Gauging of axion Symmetries and Gravity
• Lectures on Anomalies
• TASI 2003 Lectures on Anomalies
• Kaluza-Klein Dyons in String Theory
• Baby Universes, Holography, and the Swampland
• The Weak Gravity Conjecture and the Axionic Black Hole Paradox
• A Chern-Simons Pandemic
• What is the Magnetic Weak Gravity Conjecture for Axions?
• Transplanckian Censorship and Global Cosmic Strings
• Non-extremal instantons and wormholes in string theory
• Axion Mass from Magnetic Monopole Loops
• Non-extremal D-instantons
• On TCS $G_2$ manifolds and 4D Emergent Strings
• Black Holes, Moduli, and Long-Range Forces
• Theta-problem and the String Swampland
• Infinite Distance and Zero Gauge Coupling in 5d Supergravity
• Infinite Distance Limits and Information Theory
• The Weak Gravity Conjecture and BPS Particles
• Stability of BPS States and Weak Coupling Limits
• Isometries from gauge transformations

Cited by in corpus (11)

• The Weak Gravity Conjecture: A Review
• Sharpening the Distance Conjecture in Diverse Dimensions
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• The Emergence Proposal in Quantum Gravity and the Species Scale
• EFT strings and emergence
• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• Physics of Infinite Complex Structure Limits in eight Dimensions
• The Asymptotic Weak Gravity Conjecture in M-theory
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• The Inflated Chern-Simons Number in Spectator Chromo-Natural Inflation
• Axionic Festina Lente