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Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity Conjecture

Ben Heidenreich, Matthew Reece, Tom Rudelius

TL;DR

The paper argues for the Lattice Weak Gravity Conjecture as a robust, testable refinement of the Weak Gravity Conjecture, requiring a tower of charged states for all charges and predicting a finite quantum-field-theory breakdown scale at $(e M_{\rm Pl})^{-1}$. It surveys evidence from perturbative string theory and related constructions, showing the LWGC holds across diverse contexts. It derives concrete implications in axion physics, the QCD axion, AdS/CFT, and Calabi-Yau geometry, linking quantum gravity constraints to observable signatures and to mathematical structures. The authors advocate further refinement of the conjecture to capture the essential structure of string theory and to guide future theoretical and mathematical investigations.

Abstract

Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world and for pure mathematics. We sketch some implications of these ideas for models of inflation, for the QCD axion (and LIGO), for conformal field theory, and for algebraic geometry.

Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity Conjecture

TL;DR

The paper argues for the Lattice Weak Gravity Conjecture as a robust, testable refinement of the Weak Gravity Conjecture, requiring a tower of charged states for all charges and predicting a finite quantum-field-theory breakdown scale at . It surveys evidence from perturbative string theory and related constructions, showing the LWGC holds across diverse contexts. It derives concrete implications in axion physics, the QCD axion, AdS/CFT, and Calabi-Yau geometry, linking quantum gravity constraints to observable signatures and to mathematical structures. The authors advocate further refinement of the conjecture to capture the essential structure of string theory and to guide future theoretical and mathematical investigations.

Abstract

Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world and for pure mathematics. We sketch some implications of these ideas for models of inflation, for the QCD axion (and LIGO), for conformal field theory, and for algebraic geometry.

Paper Structure

This paper contains 7 sections, 5 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Applications
  3. Axion Inflation
  4. QCD Axion
  5. AdS/CFT
  6. Geometry
  7. The Nature of Quantum Gravity

Figures (2)

  • Figure 1: \ref{['sfig:KKviolation']} Kaluza-Klein reduction of theories satisfying the WGC can lead to violations in the lower dimensional theory. Sub-extremal black holes with charge-to-mass ratios in the red region are stable. \ref{['sfig:T2KK']} If the higher dimensional photon is itself a Kaluza-Klein photon, then there is an extremal charged particle of every charge, and the WGC is satisfied.
  • Figure 2: N-flation (left) and decay constant alignment (right) seek to produce a large effective decay constant from multiple sub-Planckian ones. However, the WGC implies $f_{\rm eff} \lesssim M_{\rm Planck}$ for the simplest versions of these models.

Theorems & Definitions (1)

  • Conjecture : Lattice Weak Gravity