  We explore the prospects for bounding the weak scale using the weak gravity
conjecture (WGC), addressing the hierarchy problem by violating the
expectations of effective field theory. Building on earlier work by Cheung and
Remmen, we construct models in which a super-extremal particle satisfying the
electric WGC for a new Abelian gauge group obtains some of its mass from the
Higgs, setting an upper bound on the weak scale as other UV-insensitive
parameters are held fixed. Avoiding undue sensitivity of the weak scale to the
parameters entering the bound implies that the super-extremal particle must lie
at or below the weak scale. While the magnetic version of the conjecture
implies additional physics entering around the same scale, we demonstrate that
this need not correspond to a cutoff for the Higgs potential or otherwise
trivialize the bound. We stress that linking the WGC to the weak scale
necessarily involves new light particles coupled to the Higgs, implying a
variety of experimentally accessible signatures including invisible Higgs
decays and radiative corrections in the electroweak sector. These models also
give rise to natural dark matter candidates, providing additional paths to
discovery. In particular, collective effects in the dark matter plasma may
provide a telltale sign of the Abelian gauge group responsible for bounding the
weak scale.

High Energy Physics - Phenomenology;High Energy Physics - Theory