Classification of N=6 superconformal theories of ABJM type

Abstract

Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three algebras considered by Bagger and Lambert.

18 pages

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Cited by in corpus (83)

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• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Multiple Membranes in M-theory
• Exploring Pure Spinor String Theory on AdS_4 x CP^3
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
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• A Nonperturbative Test of M2-Brane Theory
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• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Topological Twisting of Multiple M2-brane Theory
• A note on the reduction of the AdS4 x CP3 string sigma model
• Super-Yang-Mills Theory in SIM(1) Superspace
• Low-energy effective actions in three-dimensional extended SYM theories
• Generalized Conformal Symmetry and Recovery of SO(8) in Multiple M2 and D2 Branes
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• On semiclassical calculation of three-point functions in AdS_4 x CP^3
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• An associative star-three-product and applications to M two/M five-brane theory
• Dualities and flavored indices of M2-brane SCFTs
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• ABJ Quadrality
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Three lectures on 3-algebras
• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• Simplicity in the Faulkner construction
• Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories
• Supersymmetric solutions from N=5 gauged supergravity
• Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3
• Supersymmetric Chern-Simons Theory in Presence of a Boundary in the Light-Like Direction
• The Conformal Manifold of Chern-Simons Matter Theories
• Chern-Simons: Fano and Calabi-Yau
• Supersymmetric solutions from N=6 gauged supergravity
• Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal Chern-Simons-Matter Theory
• A New Three-Algebra Representation for the {\cal N}=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
• Near Flat Space limit of strings on AdS_4 x CP^3
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• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
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• ABJM Amplitudes in U-gauge and a Soft Theorem
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Charges and homologies in AdS_4/CFT_3
• Five-dimensional super Yang-Mills theory from ABJM theory
• Extension of IIB Matrix Model by Three-Algebra
• The Background Field Method for N = 2, d3 Super Chern-Simons-Matter Theories
• Reduction of the N=8 BLG and N=6 BL Theories to 2D Effective Field Theories
• Pure spinor superfields, with application to D=3 conformal models
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• Klebanov-Witten flows in M-theory
• On the Higgsing and UnHiggsing of Fano 3-Folds
• Polyakov Loops for the ABJ Theory
• Complete superspace classification of three-dimensional Chern-Simons-matter theories coupled to supergravity
• Higher Derivative Terms in Three Dimensional Supersymmetric Theories
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• Superconformal Chern-Simons theories beyond leading order
• Multiple M-branes and 3-algebras
• Algebraic vs physical N=6 3-algebras
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• Half-BPS M2-brane orbifolds
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• Mass Deformed L-BLG Theory From ABJ Theory
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