Weak Gravity Conjecture and Extremal Black Holes

TL;DR

This paper investigates quantum corrections to extremal black holes in 4d, providing evidence for the magnetic Weak Gravity Conjecture and revealing unusual entropy scaling behaviors, especially in supersymmetric contexts.

Contribution

It computes one-loop quantum corrections to black hole geometry and entropy, offering new insights into the Weak Gravity Conjecture and black hole microstates.

Findings

Fermion loops support the magnetic WGC cutoff.

Entropy corrections show unusual area scaling in certain regimes.

Supersymmetry reduces or eliminates these corrections.

Abstract

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4d. We find that fermion loops provide evidence for the necessity of the `magnetic' WGC cutoff. Moreover, for a certain regime of black holes, we find entropy corrections with unusual area scaling. The corrections are reduced when supersymmetry is present, and disappear in ${\cal N}=4$ supergravity. We further provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer.