Abstract
We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d mathcal{N}=left(1, 0right) Sp(1) gauge theory with 10 flavors and a tensor multiplet, the Nekrasov partition function of the 5d mathcal{N}=1 mathrm{S}mathrm{p}(2) gauge theory with 10 flavors, and the Nekrasov partition function of the 5d mathcal{N}=1 mathrm{S}mathrm{U}(3) gauge theory with 10 flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the SU(3) Nekrasov partition function as well as establishing the maps.
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