Towards classification of 5d SCFTs: Single gauge node

We propose a number of apparently equivalent criteria necessary for the consistency of a 5d SCFT in its Coulomb phase and use these criteria to classify 5d SCFTs arising from a gauge theory with simple gauge group. These criteria include the convergence of the 5-sphere partition function; the positivity of particle masses and monopole string tensions; and the positive definiteness of the metric in some region in the Coulomb branch. We find that for large rank classical groups simple classes of SCFTs emerge where the bounds on the matter content and the Chern-Simons level grow linearly with rank. For classical groups of rank less than or equal to 8, our classification leads to additional cases which do not fit in the large rank analysis. We also classify the allowed matter content for all exceptional groups.