ISCOs and the weak gravity conjecture bound in higher derivative theories of gravity

We study circular orbits of charged particles in spherically symmetric AdS black holes in higher derivative theories of gravity, and their limiting ISCOs (innermost stable circular orbits). The dual interpretation is in terms of heavy-light double twist conformal field theory (CFT) operators in the large spin limit, whose anomalous dimensions can be extracted from the binding energy of charged probes in the bulk, in a certain large orbit limit. Demanding the positivity of the anomalous dimensions, leads to an exact bound for the charge to mass ratio $\hat q$ of probe particles in the black hole backgrounds, which matches with the WGC bound. We find that $\hat q$ increases with the higher derivative coupling parameters, which is explicitly checked in the Gauss-Bonnet gravity. For existing computations with probe particles in AdS backgrounds, the anomalous dimension and the WGC bound we find, particularly in Gauss-Bonnet theories, are in agreement in appropriate limits with the recent computations for Schwarzschild AdS arXiv:2009.04500, charged AdS arXiv:2305.08907 and neutral Gauss-Bonnet black holes in AdS arXiv:2204.09749. Finally, we show that the ISCOs exist until the limit set by the WGC bound, with their radius decreasing with coupling parameters, which we check explicitly for the case of Gauss-Bonnet black holes in AdS.