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 how many/which 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 $T=1$.