Abstract
The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge and mass with . We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at . If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.
- Received 19 February 2014
DOI:https://doi.org/10.1103/PhysRevLett.113.051601
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