The Minimal Weak Gravity Conjecture

TL;DR

This paper proposes a minimal version of the Weak Gravity Conjecture, suggesting that towers of super-extremal particles are only necessary if required by dimensional reduction consistency, supported by evidence from string theory compactifications.

Contribution

It introduces a minimal WGC framework, establishing conditions under which super-extremal towers are necessary, and provides evidence from string theory compactifications.

Findings

Existence of a minimal radius for circle reductions in quantum gravity theories.

Super-extremal towers are only required if necessary for WGC consistency under dimensional reduction.

Evidence from F-, M-, and string theory compactifications supports the minimal WGC proposal.

Abstract

We examine the minimal constraints imposed by the Weak Gravity Conjecture (WGC) on the particle spectrum of a quantum gravity theory. Towers of super-extremal states have previously been argued to be required for consistency of the WGC under circle reduction. At the same time, there exist classes of theories where no tower of super-extremal particle states below the black hole threshold has been established with current techniques. We resolve this tension by arguing for the existence of a minimal radius for circle reductions of generic quantum gravity theories. Below this threshold, the notion of a circle compactification breaks down, bypassing the need for a tower of super-extremal states to satisfy the WGC after circle reduction. Based on this we propose that if a theory satisfies the WGC at the particle level below the black hole threshold, these states are sufficient for consistency under dimensional reduction, even in absence of a tower of super-extremal particles. Apart from general arguments, we provide independent evidence for this main result in F-, M- and string theory compactifications. According to the Emergent String Conjecture the only exception to the appearance of a minimal radius arises in asymptotically weak-coupling limits for heterotic strings, which aligns with the appearance of a weakly coupled super-extremal tower of particle states. This observation motivates a Minimal Weak Gravity Conjecture which states that towers of super-extremal particles occur if and only if they are required by consistency of the WGC under dimensional reduction.