Classification of 6d N = (1,0) gauge theories

We delineate a procedure to classify 6d N = (1, 0) gauge theories composed, in part, of a semi-simple gauge group and hypermultiplets. We classify these theories by requiring that satisfy some consistency conditions. The primary consistency condition is that the gauge anomaly can be cancelled by adding tensor multiplets which couple to the gauge fields by acting as sources of instanton strings. Based on the number of tensor multiplets required to cancel the anomaly, we conjecture that the UV completion of these consistent gauge theories (if it exists) should be either a 6d N = (1, 0) SCFT or a 6d N = (1, 0) little string theory.