On the consistency of a class of R-symmetry gauged 6D   = (1,0) supergravities

R-symmetry gauged 6D (1, 0) supergravities free from all local anomalies, with gauge groups G × G where G is the R-symmetry group and G is semisimple with rank greater than one, and which have no hypermultiplet singlets, are extremely rare. There are three such models known in which the gauge symmetry group is G ₁ × G ₂ × U(1) , where the first two factors are $$ , G ₂ × E ₇ and F ₄ × Sp(9). These are models with single tensor multiplet, and hyperfermions in the (1, 912), (14, 56) and (52, 18) dimensional representations of G ₁ × G ₂, respectively. So far, it is not known if these models follow from string theory. We highlight key properties of these theories, and examine constraints which arise from the consistency of the quantization of anomaly coefficients formulated in their strongest form by Monnier and Moore. Assuming that the gauged models accommodate dyonic string excitations, we find that these constraints are satisfied only by the model with the F ₄ × Sp(9) × U(1) symmetry. We also discuss aspects of dyonic strings and potential caveats they may pose in applying the stated consistency conditions to the R-symmetry gauged models.