Discrete Gauge Symmetries and the Weak Gravity Conjecture

Abstract

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle's mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that `gravity is the weakest force'. Here, we take a step towards making this expectation more precise by studying ${\mathbb{Z}}_N$ and ${\mathbb{Z}}_2^N$ gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to $M_{Pl}$.

15 pages; introduction and conclusions extended; matches published version

References in corpus (13)

• On the Geometry of the String Landscape and the Swampland
• Causality, Analyticity and an IR Obstruction to UV Completion
• Tensionless Strings and the Weak Gravity Conjecture
• The Weak Gravity Conjecture in three dimensions
• Natural Inflation and Quantum Gravity
• Infrared Consistency and the Weak Gravity Conjecture
• A Holographic Derivation of the Weak Gravity Conjecture
• Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
• Weak gravity conjecture in the asymptotical dS and AdS background
• A proof of the weak gravity conjecture
• Gravity Cutoff in Theories with Large Discrete Symmetries
• Rescuing Massive Photons from the Swampland
• Properties of Discrete Black Hole Hair

Cited by in corpus (13)

• Lectures on the Swampland Program in String Compactifications
• The Weak Gravity Conjecture: A Review
• Swampland Conjectures for Strings and Membranes
• Topological Operators and Completeness of Spectrum in Discrete Gauge Theories
• Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• Discrete Symmetries, Weak Coupling Conjecture and Scale Separation in AdS Vacua
• Approximate Symmetries and Gravity
• The Weak Scale from Weak Gravity
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation
• Discrete Symmetries in Dimer Diagrams
• Implications of the weak gravity conjecture in anomalous quiver gauge theories