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

TL;DR

This paper explores the Weak Gravity Conjecture and introduces the Lattice Weak Gravity Conjecture, linking quantum gravity, string theory, and algebraic geometry with testable implications for physics and mathematics.

Contribution

It proposes the Lattice Weak Gravity Conjecture, extending the original conjecture and connecting quantum gravity constraints with algebraic geometry and other fields.

Findings

The Lattice Weak Gravity Conjecture holds in various string theory models.

It implies a cutoff for quantum field theories.

Testable consequences for physics and mathematics are identified.

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.