Towards a proof of the Weak Gravity Conjecture

TL;DR

This paper explores the Weak Gravity Conjecture (WGC) using holography and AdS/CFT correspondence, linking it to thermalization in boundary CFTs and verifying its validity through thermodynamic analysis.

Contribution

It proposes a holographic formulation of the WGC and connects it to the thermalization properties of boundary conformal field theories, providing a new perspective on its proof.

Findings

WGC can be expressed in terms of AdS/CFT correspondence.

Thermalization properties of boundary CFTs relate to the WGC.

Thermodynamic analysis supports the validity of the WGC.

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.