The Weak Gravity Conjecture, Naturalness, and Discrete Gauge Symmetries

The most studied part of the Swampland program is the Weak Gravity Conjecture (WGC), which for massless U(1) gauge bosons states that the force between two charged particles must be strictly greater than the gravitational attraction. I first discuss the prospects for the WGC to set an upper bound on the value of the weak scale parametrically below the scale at which radiative corrections to the Higgs potential are cut off, thereby addressing the hierarchy problem by violating the expectations of effective field theory. Potential experimentally testable implications of a WGC-based theory of naturalness, including modifications to Higgs properties, as well as implications for dark matter are examined.

 

In the second part of the talk, I will discuss how it is natural to expect that a non-trivial version of the WGC also applies in the context of discrete gauge symmetries, despite there being no associated massless vector, therefore pushing the WGC beyond the slogan that ‘gravity is the weakest force’.