We present a semiclassical proof of the weak gravity conjecture in @math spacetime dimensions for scalar matter gauged under a @math gauge group. We compute the non-perturbative macroscopic entropy of a scalar field in an extremal black hole background at the level of linearized backreaction on the metric. The scalar field is assumed to violate or saturate the weak gravity conjecture. The scalar contributes a logarithmic correction to the entropy in the black hole geometry that outgrows the classical contribution. We demonstrate that the entropy of the gauged scalar violates the generalized second law in the limit of large black hole charge. Our result suggests that entropy inequalities may directly discriminate between effective field theories that live in the landscape versus the swampland.
Qualitatively similar results to our entropy calculation appear in @cite_17 . However, not all of their quantitative results match ours exactly. We believe that this results from the formalism they use to calculate the entropy of the black hole, which is not exactly equivalent to ours. We also believe that their conclusions and interpretation of results differ significantly enough from our own. Moreover, they do not attempt to prove the weak gravity conjecture using entropy inequalities, although they allude to this possibility.
@cite_17
2550488390 2045285156 2022232745 1975244148
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 @math 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. Abstract Strominger and Vafa have used D-brane technology to identify and precisely count the degenerate quantum states responsible for the entropy of certain extremal, BPS-saturated black holes. Here we give a Type-II D-brane description of a class of extremal and non-extremal five-dimensional Reissner-Nordstrom solutions and identify a corresponding set of degenerate D-brane configurations. We use this information to do a string theory calculation of the entropy, radiation rate and “Hawking” temperature. The results agree perfectly with standard Hawking results for the corresponding nearly extremal Reissner-Nordstrom black holes. Although these calculations suffer from open-string strong coupling problems, we give some reasons to believe that they are nonetheless qualitatively reliable. In this optimistic scenario there would be no “information loss” in black hole quantum evolution. Abstract Entropy bounds render quantum corrections to the cosmological constant Λ finite. Under certain assumptions, the natural value of Λ is of order the observed dark energy density ∼10 −10 eV 4 , thereby resolving the cosmological constant problem. We note that the dark energy equation of state in these scenarios is w ≡ p ρ =0 over cosmological distances, and is strongly disfavored by observational data. Alternatively, Λ in these scenarios might account for the diffuse dark matter component of the cosmological energy density. We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.