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The weak gravity conjecture and the shear viscosity to entropy density boundplace constraints on low energy effective field theories that may help todistinguish which theories can be UV completed. Recently, there have beensuggestions of a possible correlation between the two constraints. In someinteresting cases, the behavior was precisely such that the conjectures weremutually exclusive. Motivated by these works, we study the mass to charge andshear viscosity to entropy density ratios for charged AdS5 black branes, whichare holographically dual to four-dimensional CFTs at finite temperature. Westudy a family of four-derivative and six-derivative perturbative correctionsto these backgrounds. We identify the region in parameter space where the twoconstraints are satisfied and in particular find that the inclusion of thenext-to-leading perturbative correction introduces wider possibilities for thesatisfaction of both constraints.

The Weak Gravity Conjecture and the Viscosity Bound with Six-Derivative Corrections