Towards a proof of the Weak Gravity Conjecture

Abstract: The Weak Gravity Conjecture (WGC) asserts a powerful consistency condition on gauge theories coupled to gravity, and it is widely believed that its proof will shed light on the quantum origin of gravitational interactions. Holography, and in particular the AdS/CFT correspondence, is a well-suited tool by means of which it is possible to explore the world of gravity. From the holographic perspective, gravity is an emergent statistical phenomenon, and the laws of gravitation can be recast as the laws of thermodynamics. It is interesting to ask whether the WGC can be formulated in terms of the AdS/CFT correspondence. A positive answer is given: The WGC in the bulk is linked to the thermalization properties of the CFT living on the boundary. The latter is related to the Sachdev-Ye-Kitaev model of strange metals. In the thermodynamic picture, the validity of the WGC is verified.