Enumerating 6D supergravities with T ≤ 1

The space of 6D supergravities with minimal supersymmetry is greatly constrained by anomaly cancellation. Nevertheless, a large number of models satisfy all low-energy consistency conditions and in this work we make progress towards exhaustively enumerating all anomaly-free models with at most one tensor multiplet. Generalizing previous techniques, we describe a general algorithm using multi-hypergraphs and simplicial complexes to systematically enumerate anomaly-free models with gauge groups of any number of simple factors and with hypermultiplets falling into any representations. Using these new ideas, we obtain a complete list of anomaly-free models for T ≤ 1, the only simplifying assumption being that the gauge group contains no U(1), SU(2), SU(3) or Sp(2) factors. We also study which and how many models in this ensemble satisfy several UV and swampland bounds which have been proposed and previously utilized to great effect, finding that none are ruled out for T = 0 and ≈ 50% are inconsistent with quantum gravity for T = 1.