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\(\mathcal N= 6\) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals. (English) Zbl 1245.81130
Summary: We construct three dimensional Chern-Simons-matter theories with gauge groups \(U(N) \times U(N)\) and \(SU(N) \times SU(N)\) which have explicit \(\mathcal N = 6\) superconformal symmetry. Using brane constructions we argue that the \(U(N) \times U(N)\) theory at level \(k\) describes the low energy limit of \(N\) M2-branes probing a \(C^{4}/Z_{k}\) singularity. At large \(N\) the theory is then dual to M-theory on \(AdS_{4} \times S^{7}/Z_{k}\). The theory also has a ’t Hooft limit (of large \(N\) with a fixed ratio \(N/k\)) which is dual to type IIA string theory on \(AdS_{4} \times \mathbb{C}\mathbb{P}^{3}\). For \(k = 1\) the theory is conjectured to describe \(N\) M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in \(d = 3\) gauge theories. When the gauge group is \(SU(2) \times SU(2)\) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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