  We perform a global analysis of the space of consistent 6D quantum gravity
theories with N = 1 supersymmetry, including models with multiple tensor
multiplets. We prove that for theories with fewer than T = 9 tensor multiplets,
a finite number of distinct gauge groups and matter content are possible. We
find infinite families of field combinations satisfying anomaly cancellation
and admitting physical gauge kinetic terms for T > 8. We find an integral
lattice associated with each apparently-consistent supergravity theory; this
lattice is determined by the form of the anomaly polynomial. For models which
can be realized in F-theory, this anomaly lattice is related to the
intersection form on the base of the F-theory elliptic fibration. The condition
that a supergravity model have an F-theory realization imposes constraints
which can be expressed in terms of this lattice. The analysis of models which
satisfy known low-energy consistency conditions and yet violate F-theory
constraints suggests possible novel constraints on low-energy supergravity
theories.
