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Note on a Paper by Ooguri and Vafa

In a recent paper, Ooguri and Vafa [arXiv:1610.04564] argued that a mild extension of the Weak Gravity conjecture\cite{weakgrav} led to the conclusion that the only models of quantum gravity in AdS space with "radius large compared to the string scale" were models with exact AdS-SUSY. This note clarifies certain obscure parts of their argument by reinterpreting it as a statement about brane configurations in flat space. In that context the statement is that stable non-supersymmetric configurations of branes are characterized by charges in the torsion subgroup of K-theory and their only long range fields are gravitational and scalar. The field equations do not have large radius near horizon AdS solutions. Instead the horizons are Schwarzschild black branes. This leads us to conjecture that for $d \leq 11$ the K theory charges are bounded by a small integer, and there can be no large gravitational back reaction in the near horizon limit, for stable configurations. Unbounded values of these discrete charges would violate the Covariant Entropy Bound. We discuss a counterexample to the conjecture in $AdS_3$. We find similar counterexamples in higher dimensional AdS spaces, but argue that none of them lead to SUSY violating models of quantum gravity in Minkowski space.