Global aspects of the space of 6D N=1 supergravities

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.