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

Abstract

We argue the equivalence between the infrared conformal field theory of the 3d $\mathcal{N}=8$ supersymmetric Yang-Mills theories of ABCD ($U(N),SO(2N+1),Sp(2N),O(2N)$) gauge groups and the ABJ(M) theories of $U(N{)}_k\times U(\tilde{N}{)}_{-k}$ for $k=1,2$. We support this duality by comparing the superconformal index of the IR limit of these super Yang-Mills theories and that of those ABJ(M) models. Especially we find the match between two indices of (mirror dual of) 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 additional fundamental hyper-multiplets and infer the large N limit of $\mathcal{N}=8$ ABCD theories themselves, finding the expected gravitational duals. With the additional 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 matter theories for $\mathcal{N}=4$ Yang-Mills theories related by mirror symmetry.

46 pages, 4 figures, references added

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• Algebraic structures on parallel M2-branes
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
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• Generalized Superconformal Index for Three Dimensional Field Theories
• Superconformal indices of three-dimensional theories related by mirror symmetry
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Cited by in corpus (14)

• N=3 four dimensional field theories
• Aharony Dualities for 3d Theories with Adjoint Matter
• Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
• Evidence for Aharony duality for orthogonal gauge groups
• Quantum vortices, M2-branes and black holes
• Amplitudes of 3d Yang Mills Theory
• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Duality between N=5 and N=6 Chern-Simons matter theory
• Lectures on 4d N=1 dynamics and related topics
• Flows between Dualities for 3d Chern-Simons Theories
• Factorization of the 3d superconformal index
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• $\mathcal{N}=3$ four dimensional field theories