Six-dimensional supergravity theories are strongly constrained by anomaly cancellation, thereby providing an interesting playground to study the boundaries of the string theory landscape. In the present talk, I will describe new consistency constraints on six-dimensional supergravity theories that depend on the global structure of the gauge group. These new constraints are all satisfied in 6d supergravity theories realizable as string theory/F-theory
vacua. An interesting side result is an identification of the global form of the gauge group associated to F-theory compactifications to six-dimensions. This is joint work with Gregory Moore and Daniel Park (1711.04777).