The String Landscape, Black Holes and Gravity as the Weakest Force

TL;DR

The paper argues that gravity is the weakest force in quantum gravity, predicting a UV cutoff Λ ∼ g M_Pl and the existence of a light charged state with m ≤ Λ in any theory with a U(1) gauge field. It sharpens this into a mass/charge bound, requiring states with (M/Q) smaller than extremal black holes to allow BHs to decay, with supporting checks from string theory and generalizations to higher-form gauge fields. The authors test the conjecture in concrete string vacua, relate it to finiteness of stable states and the absence of global symmetries, and discuss broader implications for UV physics, inflation, and potential positivity constraints on EFT operators. They also outline possible experimental signatures via ultra-weak gauge forces and show how AdS/CFT may provide further avenues for proof or refutation.

Abstract

We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Lambda=g M_{Pl}, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Lambda. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light "elementary" electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.