NUT charge weak gravity conjecture from dimensional reduction

We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole weak gravity conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.

Figure 1

Sub-extremal black hole regions for: blackplotblue two-derivative solutions and blackplotorange four-derivative corrected solutions. Left: $(Q_0,P_0)$ black hole satisfying WGC bound (17). Center: $(Q_0,P_1)$ black hole satisfying WGC bound (10). Right: $(Q_1,P_0)$ black hole satisfying the WGC bounds implied by (21), with $c_1=c_2=c_4=c_5=0$ and $c_3>0$.