Abstract
The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn’t happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version of the WGC, which reduces to the usual statement at weak coupling. The argument is general, and it does not rely on either supersymmetry or a particular UV completion, assuming only the validity of Einsteinian gravity, effective field theory, and holography. The pathology is related to the development of an infinite throat in the near-horizon region of the extremal solutions, which suggests a connection to the ER=EPR proposal.
Highlights
Against de Sitter, and [33] for arguments supporting the conjecture)
The vanishing photon mass prediction mentioned above involves the Weak Gravity Conjecture (WGC) as well. All of this makes the WGC one of the most interesting Swampland constraints, but why should it be true? On top of the fact that it seems to be satisfied in string compactifications, sometimes in very nontrivial ways [84,85,86], there is a heuristic argument that extremal black holes should be unstable [46, 87]
It is often said that consistent quantum theories of gravity must satisfy the WGC in order to avoid stable extremal black holes, but it was never clear precisely what is wrong with these
Summary
– Subsection 2.1 focuses on (charged) black holes and how to relate them to CFT quantities. – Subsection 2.2 discusses the thermofield double formalism and near-horizon symmetries of extremal black holes. – Subsection 2.3 is a lightning review on entanglement entropy (EE) and holographic entanglement entropy computations. It discusses the holographic EE computation for the black holes of interest. – In subsection 3.1, a contradiction is presented between the holographic EE calculation and a quantum information theorem. – Subsection 3.2 presents the main result coming out of the previous subsection, discussing how it reduces to the standard WGC in both supersymmetric and nonsupersymmetric cases.
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