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2017

A proof of the weak gravity conjecture

Hod, Shahar

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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.

A proof of the weak gravity conjecture · Around

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This mass-charge relation is certainly true in our world. In particular, the electron is characterized by the dimensionless mass-to-charge ratio m e / | q e | ≃ 4.9 × 10 − 22 ≪ 1 m_{e}/|q_{e}|\simeq 4.9\times 10^{-22}\ll 1

Cited in the paper.

We shall henceforth use natural units in which G = c = ℏ = k B = 1 G=c=\hbar=k_{\text{B}}=1 . Note that in these units q q and m m have the dimensions of length -1

Cited in the paper.

L. Susskind, arXiv:hep-th/9501106

Cited in the paper.

Note, in particular, that the mass-charge inequality ( 1

Cited in the paper.

The generalized second law of thermodynamics Bek1 states that the total entropy in a coupled black-hole-matter system is an irreducible physical quantity

Cited in the paper.

Here A A is the black-hole surface area

Cited in the paper.