# A proof of the weak gravity conjecture

## TL;DR

This paper provides a proof of the weak gravity conjecture by deriving it from Bekenstein's generalized second law of thermodynamics, linking quantum gravity constraints to thermodynamic principles.

## Contribution

It offers the first proof of the weak gravity conjecture based on fundamental thermodynamic laws, strengthening its theoretical foundation.

## Key findings

- The weak gravity conjecture can be derived from the generalized second law of thermodynamics.
- The mass-charge bound $m/m_{P}<q$ follows from thermodynamic considerations.
- Supports the conjecture's validity within quantum gravity frameworks.

## Abstract

The weak gravity conjecture suggests that, in a self-consistent theory of quantum gravity, the strength of gravity is bounded from above by the strengths of the various gauge forces in the theory. In particular, this intriguing conjecture asserts that in a theory describing a U(1) gauge field coupled consistently to gravity, there must exist a particle whose proper mass is bounded (in Planck units) by its charge: $m/m_{\text{P}}<q$. This beautiful and remarkably compact conjecture has attracted the attention of physicists and mathematicians over the last decade. It should be emphasized, however, that despite the fact that there are numerous examples from field theory and string theory that support the conjecture, we still lack a general proof of its validity. In the present Letter we prove that the weak gravity conjecture (and, in particular, the mass-charge upper bound $m/m_{\text{P}}<q$) can be inferred directly from Bekenstein's generalized second law of thermodynamics, a law which is widely believed to reflect a fundamental aspect of the elusive theory of quantum gravity.