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.

21 pages, v2: minor changes

References in corpus (15)

• 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
• A Natural Framework for Chaotic Inflation
• Super-Planckian Spatial Field Variations and Quantum Gravity
• Unbroken B-L Symmetry
• The Weak Gravity Conjecture in three dimensions
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Three-Form Gauging of axion Symmetries and Gravity
• Lectures on Anomalies
• TASI 2003 Lectures on Anomalies
• Axion Mass from Magnetic Monopole Loops
• Infinite Distance Limits and Information Theory
• Stability of BPS States and Weak Coupling Limits
• The Weak Gravity Conjecture and BPS Particles

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