The UV Fate of Anomalous $U(1)$s and the Swampland

Understand

Massive $U(1)$ gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity.

• We study four-dimensional, chiral $U(1)$ gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions.
• We show that such theories require to be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled -- a St\"uckelberg limit does not exist.
• When the infrared fermion spectrum contains a mixed $U(1)$-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass.