A new 5d description of 6d D-type minimal conformal matter

We propose a new 5d description of the circle-compactified 6d $(D_{N+4}, D_{N+4})$ minimal conformal matter theory which can be approached by the 6d $\mathcal{N}=(1,0)$ $Sp(N)$ gauge theory with $N_f=2N+8$ flavors and one tensor multiplet. Compactifying the brane set-up for the 6d theory, we arrive at a 5-brane Tao diagram for 5d $\mathcal{N}=1$ $SU(N+2)$ theory of the vanishing Chern-Simons level with $2N+8$ flavors. We conjecture that the 6d theory is recovered as the UV fixed point of this 5d theory. We show that the global symmetry of this 5d theory is $SO(4N+16)$ identical to that of the 6d theory by analyzing the 7-brane monodromy. By using the Tao diagram, we also find the instanton fugacity is exactly given by the circle radius. By decoupling flavors in this 5d theory, one can obtain all the 5d $SU(N+2)$ gauge theories of various Chern-Simons levels and corresponding enhanced global symmetries at the 5d UV fixed point.