Charge lattices and consistency of 6D supergravity

We extend the known consistency conditions on the low-energy theory of six-dimensional supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Γ for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Γ. The condition that this sublattice can be extended to a self-dual lattice Γ leads to a strong constraint on theories that otherwise appear to be self-consistent.