Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Naturalness and the Weak Gravity Conjecture

Clifford Cheung, Grant N. Remmen

TL;DR

This work analyzes the tension between naturalness and the weak gravity conjecture (WGC) in Abelian gauge theories, including extensions to product gauge groups. It shows that radiative stability of scalars and the WGC imply a delicate interplay: reconciling naturalness with $z_i = q_i m_{ m Pl}/m_i$ requires either a Higgs phase or a low cutoff $ abla o m_{ m Pl}$, and it introduces a convex-hull criterion for multiple $U(1)$ factors, demanding that the convex hull of $igl\{oldsymbol{z}_i, -oldsymbol{z}_iigrig r$ contain the unit ball. The paper proposes experimental tests via millicharged forces, showing that naturalness would predict either a low cutoff or new states, while the discovery of millicharged interactions or a fifth force could falsify naturalness or, in a strong interpretation, string theory’s four-dimensional QFT breakdown. Overall, the work highlights a concrete, testable link between UV consistency conditions in quantum gravity and low-energy naturalness, with clear predictions for multi- U(1) sectors and millicharged phenomena.

Abstract

The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge $q$ and mass $m$ with $q>m/m_{\rm Pl}$. We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at $Λ\sim q m_{\rm Pl}$. If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.

Naturalness and the Weak Gravity Conjecture

TL;DR

This work analyzes the tension between naturalness and the weak gravity conjecture (WGC) in Abelian gauge theories, including extensions to product gauge groups. It shows that radiative stability of scalars and the WGC imply a delicate interplay: reconciling naturalness with requires either a Higgs phase or a low cutoff , and it introduces a convex-hull criterion for multiple factors, demanding that the convex hull of contain the unit ball. The paper proposes experimental tests via millicharged forces, showing that naturalness would predict either a low cutoff or new states, while the discovery of millicharged interactions or a fifth force could falsify naturalness or, in a strong interpretation, string theory’s four-dimensional QFT breakdown. Overall, the work highlights a concrete, testable link between UV consistency conditions in quantum gravity and low-energy naturalness, with clear predictions for multi- U(1) sectors and millicharged phenomena.

Abstract

The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge and mass with . We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at . If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.

Paper Structure

This paper contains 5 sections, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Evidence for the WGC
  3. The Limits of Naturalness
  4. More Forces, More Particles
  5. The Hierarchy Problem

Figures (1)

  • Figure 1: Vectors representing charge-to-mass ratios for two species charged under two Abelian gauge symmetries. When the convex hull defined by these vectors contains the unit ball, then extremal black holes can decay to particles and the condition of the WGC is satisfied.