Understand
In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is "generic," in the sense that other "exotic" matter representations require more fine tuning.
- From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and $\operatorname{U}(1)$ factors.
- These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types.
- The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple $\operatorname{U}(1)$ factors and provides a useful framework for analyzing the 6D "swampland" of apparently consistent low-energy theories that cannot be realized through known string constructions.