Testing 5d-6d dualities with fractional D-branes

6d scfts compactified on a circle can often be studied from nonperturbative 5d super-yang-mills theories, using instanton solitons. however, the 5d yang-mills theories with 6d uv fixed points frequently have too many hypermultiplet matters, which makes it difficult to use the adhm techniques for instantons. with the examples of 6d $$ mathcal{n}=left(1, 0right) $$ scfts with sp(n) gauge symmetry and 2n + 8 fundamental hypermultiplets, we show that one can still make rigorous studies of these 5d-6d relations in the ‘fractional d-brane sectors’. we test the recently proposed 5d duals given by sp(n + 1) gauge theories, and compare their instanton partition functions with the elliptic genera of 6d self-dual strings.