  We analyze the anomaly constraints on 6D supergravity theories with a single
abelian U(1) gauge factor. For theories with charges restricted to $q = \pm1,
\pm2$ and no tensor multiplets, anomaly-free models match those models that can
be realized from F-theory compactifications almost perfectly. For theories with
tensor multiplets or with larger charges, the F-theory constraints are less
well understood. We show, however, that there is an infinite class of distinct
massless charge spectra in the "swampland" of theories that satisfy all known
quantum consistency conditions but do not admit a realization through F-theory
or any other known approach to string compactification. We also compare the
spectra of charged matter in abelian theories with those that can be realized
from breaking nonabelian SU(2) and higher rank gauge symmetries.
