A New Spin on the Weak Gravity Conjecture

TL;DR

This paper reformulates the Weak Gravity Conjecture as an integrated stress tensor condition, extending it to rotating black holes and deriving new positivity bounds on higher-dimensional Wilson coefficients.

Contribution

It introduces a unified stress tensor condition for the Weak Gravity Conjecture applicable to charged and rotating black holes, and derives stronger bounds on higher-dimensional operators.

Findings

The spinning version of the Weak Gravity Conjecture is proven using the c-theorem.

Positivity bounds on five-dimensional Wilson coefficients are strengthened.

The reformulation applies to various black hole solutions, including boosted black strings.

Abstract

The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the $c$-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a $\text{BTZ}\times S^2$ near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.