The Weak Gravity Conjecture and the Axionic Black Hole Paradox

TL;DR

The paper investigates whether a perturbatively massless 2-form (dual to an axion) can be consistently coupled to quantum gravity at small $f$ without light charged objects, by studying axionic black holes that carry a horizon Wilson line $b=\int B_2$. It develops a 2-form Weak Gravity-type argument by analyzing late-stage BH evaporation, deriving parametric bounds on the string tension that depend on the evaporation dynamics, and explores infrared/non-perturbative effects as well as quantum-vs-classical aspects of the hair. In aligned multi-axion setups, the work highlights how light monopoles carrying fractional axion charge may discharge hair, offering an alternative to ultra-light strings. Overall, the results provide a 2-form WGC intuition, connect weak coupling to the necessity of light states, and suggest directions for extending the analysis to gauged or higher-dimensional scenarios.

Abstract

In theories with a perturbatively massless 2-form (dual to an axion), a paradox may arise in the process of black hole evaporation. Schwarzschild black holes can support a non-trivial Wilson-line-type field, the integral of the 2-form around their horizon. After such an 'axionic black hole' evaporates, the Wilson line must be supported by the corresponding 3-form field strength in the region formerly occupied by the black hole. In the limit of small axion decay-constant f, the energy required for this field configuration is too large. The natural resolution is through the presence of light strings, which allow the black hole to "shed" its axionic hair sufficiently early. This gives rise to a new Weak-Gravity-type argument in the 2-form context: Small coupling, in this case f, enforces the presence of light strings or a low cutoff. We also discuss how this argument may be modified in situations where the weak coupling regime is achieved in the low-energy effective theory through an appropriate gauging of a model with a vector field and two 2-forms.

Figures (1)

• Figure 1: Field space of $b_1$ and $b_2$. The subspace parametrized by the light axion for $N=3$ is shown. The arrow denotes the point associated with an $S^2$ loop around an anti-monopole.