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We argue the equivalence between the infrared conformal field theory of the3d $\mathcal{N}=8$ supersymmetric Yang-Mills theories of ABCD ($U(N), SO(2N+1),Sp(2N), O(2N)$) gauge groups and the ABJ(M) theories of $U(N)_k\times U(\tildeN)_{-k}$ for $k=1,2$. We support this duality by comparing the superconformalindex of the IR limit of these super Yang-Mills theories and that of thoseABJ(M) models. Especially we find the match between two indices of (mirror dualof) the $\mathcal{N}=8$ U(N) SYM and of $U(N)_1\times U(N)_{-1}$ ABJM model.Also we take large $N$ limit of ABCD super Yang-Mills theories with additionalfundamental hyper-multiplets and infer the large N limit of $\mathcal{N}=8$ABCD theories themselves, finding the expected gravitational duals. With theadditional input on finite N, we argue the equivalence of Yang-Mills and ABJ(M)theories for all N. We further explore similar dualities to Chern-Simons mattertheories for $\mathcal{N}=4$ Yang-Mills theories related by mirror symmetry.

ABCD of 3d ${\cal N}=8$ and 4 Superconformal Field Theories