Three-Algebras and N=6 Chern-Simons Gauge Theories

Abstract

We derive the general form for a three-dimensional scale-invariant field theory with N=6 supersymmetry, SU(4) R-symmetry and a U(1) global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not antisymmetric. For a specific choice of 3-algebra we obtain the N=6 theories that have been recently proposed as models for M2-branes in an R^8/Z_k orbifold background.

19 pages. Typos corrected

References in corpus (37)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• Fractional M2-branes
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• Membranes on an Orbifold
• Selfdual strings and loop space Nahm equations
• Constraining Maximally Supersymmetric Membrane Actions
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• M2 to D2 revisited
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• M2-branes, 3-Lie Algebras and Plucker relations
• Supersymmetric Yang-Mills Theory From Lorentzian Three-Algebras
• M2-branes on M-folds
• Mass-Deformed Bagger-Lambert Theory and its BPS Objects
• Bagger-Lambert Theory for General Lie Algebras
• Ghost-Free Superconformal Action for Multiple M2-Branes
• D2 to D2
• Multiple M2-branes and the Embedding Tensor
• Multiple Membranes from Gauged Supergravity
• A New N=4 Membrane Action via Orbifold
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Matrix Theory of Type IIB Plane Wave from Membranes
• Coulomb Branch of the Lorentzian Three Algebra Theory
• Kac-Moody Extensions of 3-Algebras and M2-branes
• Metric Lie 3-algebras in Bagger-Lambert theory
• Prolongations of Lie algebras and applications
• On relating multiple M2 and D2-branes
• A Non-Supersymmetric Large-N 3D CFT And Its Gravity Dual

Cited by in corpus (190)

• n-ary algebras: a review with applications
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• Three-dimensional N=6 SCFT's and their membrane dynamics
• Scattering Amplitudes
• The AdS4/CFT3 algebraic curve
• Classification of N=6 superconformal theories of ABJM type
• Generation of Matrix Models by W-operators
• On the Lie-algebraic origin of metric 3-algebras
• Multiple M2-branes and Generalized 3-Lie algebras
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Multiple Membranes in M-theory
• Membranes with a boundary
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
• ABJM models in N=3 harmonic superspace
• Boundary Conditions for Interacting Membranes
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• Beables/Observables in Classical and Quantum Gravity
• Brane Effective Actions, Kappa-Symmetry and Applications
• N=4 Chern-Simons theories and wrapped M-branes in their gravity duals
• Superconformal Chern-Simons Theories and the Squashed Seven Sphere
• Unitary Integrals and Related Matrix Models
• From N M2's to N D2's
• Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories
• The tensor hierarchy algebra
• A Nonperturbative Test of M2-Brane Theory
• On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
• M2-Branes and Background Fields
• The Power of the Higgs Mechanism: Higher-Derivative BLG Theories
• Superfield actions for N=8 and N=6 conformal theories in three dimensions
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Marginal Deformations and 3-Algebra Structures
• Tensor hierarchies, Borcherds algebras and E11
• Nijenhuis operators on $n$-Lie algebras
• Topological branes, p-algebras and generalized Nahm equations
• Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes
• On Half-BPS States of the ABJM Theory
• Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace
• N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators
• Three-algebras, triple systems and 3-graded Lie superalgebras
• N=6 conformal supergravity in three dimensions
• On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification
• Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory
• Three-dimensional topologically gauged N=6 ABJM type theories
• Symplectic, product and complex structures on 3-Lie algebras
• Higher Derivative Supergravities in Diverse Dimensions
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• A new integral formula for supersymmetric scattering amplitudes in three dimensions
• Some BPS configurations of the BLG Theory
• Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
• Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
• Topological Twisting of Multiple M2-brane Theory
• Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling
• Exceptional geometry and Borcherds superalgebras
• Monopole operators in N=4 Chern-Simons theories and wrapped M2-branes
• Generalized Conformal Symmetry and Recovery of SO(8) in Multiple M2 and D2 Branes
• Superconformal Indices for Orbifold Chern-Simons Theories
• Topological Chern-Simons Sigma Model
• Supergravity dual of Chern-Simons Yang-Mills theory with N=6,8 superconformal IR fixed point
• Monopoles, three-algebras and ABJM theories with $\mathbb{N}=5,6,8$ supersymmetry
• A new approach to representations of $3$-Lie algebras and abelian extensions
• Octonions, G_2 and generalized Lie 3-algebras
• A No-Go Theorem for M5-brane Theory
• Superpotentials for superconformal Chern-Simons theories from representation theory
• M5-brane Solution in ABJM Theory and Three-algebra
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• M-Theory and Maximally Supersymmetric Gauge Theories
• N=6 Membrane Worldvolume Superalgebra
• Lie 2-algebra models
• An associative star-three-product and applications to M two/M five-brane theory
• Precision Spectroscopy and Higher Spin symmetry in the ABJM model
• Nambu Bracket for M Theory
• M5 brane from mass deformed BLG theory
• The ABJM Model is a Higher Gauge Theory
• Topological M-Strings and Supergroup WZW Models
• Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• The two-loop six-point amplitude in ABJM theory
• Non-Lorentzian RG flows and Supersymmetry
• Three lectures on 3-algebras
• Simplicity in the Faulkner construction
• M2-brane Flows and the Chern-Simons Level
• M2-branes on a resolved $C_4/Z_4$
• Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3
• Supersymmetry and DLCQ Limit of Lie 3-algebra Model of M-theory
• Comments on Baryon-like Operators in N=6 Chern-Simons-matter theory of ABJM
• Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories
• Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories
• δ-derivations of n-ary algebras
• Supersymmetric solutions from N=5 gauged supergravity
• Interaction between M2-branes and Bulk Form Fields
• Cohomology of Filippov algebras and an analogue of Whitehead's lemma
• $3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras
• Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories
• Ternutator Identities
• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
• Supersymmetric solutions from N=6 gauged supergravity
• A New Three-Algebra Representation for the {\cal N}=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
• Abelian Vortex in Bagger-Lambert-Gustavsson Theory
• Deconstructing graviphoton from mass-deformed ABJM
• Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
• Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal Chern-Simons-Matter Theory
• On thermodynamics of N=6 superconformal Chern-Simons theories at strong coupling
• N=5 three-algebras and 5-graded Lie superalgebras
• Light-cone analysis of ungauged and topologically gauged BLG theories
• Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter
• On non-abelian extensions of 3-Lie algebras
• Dynamical supersymmetry in maximally supersymmetric gauge theories
• A non-associative quaternion scalar field theory
• Irreducible Highest Weight Representations Of The Simple n-Lie Algebra
• Membrane Dynamics in Three dimensional N=6 Supersymmetric Chern-Simons Theory
• ABJM Amplitudes in U-gauge and a Soft Theorem
• Self-dual String and Higher Instanton Solutions
• On a class of n-Leibniz deformations of the simple Filippov algebras
• Charges and homologies in AdS_4/CFT_3
• Coset for Hopf fibration and Squashing
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Three-Algebra BFSS Matrix Theory
• Remark About Scaling Limit of ABJ Theory
• Two-loop low-energy effective action in Abelian supersymmetric Chern-Simons matter models
• Five-dimensional super Yang-Mills theory from ABJM theory
• BLG theory with generalized Jordan triple systems
• Marginal Fluctuations as Instantons on M2/D2-Branes
• Extension of IIB Matrix Model by Three-Algebra
• M5-branes in ABJM theory and Nahm equation
• Magnetic Domains
• Superalgebra Realization of the 3-algebras in N=6, 8 Chern-Simons-matter Theories
• The Background Field Method for N = 2, d3 Super Chern-Simons-Matter Theories
• Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories
• A N=8 action for multiple M2-branes with an arbitrary number of colors
• Ground Ring of Alpha-Symmetries and Sequence of RNS String Theories
• Renormalization Group Improvement of the Superpotential for the N=2 Chern-Simons-matter model
• Wilson Loops from D-branes in AdS(4) X CP**3 with B-NS Holonomy
• Open M2-branes with Flux and Modified Basu-Harvey Equation
• Fusion of Superalgebras and D=3, N=4 Quiver Gauge Theories
• M-Brane Models and Loop Spaces
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra
• Topics on n-ary algebras
• Exceptional Lie algebras and M-theory
• 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
• A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1
• Covariantly Constant Curvature Tensors and D=3, N=4, 5, 8 Chern-Simons Matter Theories
• From Basu-Harvey to Nahm equation via 3-Lie bialgebra
• M2 to D2 and vice versa by 3-Lie and Lie bialgebra
• Higher identities for the ternary commutator
• Klebanov-Witten flows in M-theory
• Aspects of Supersymmetry in Multiple Membrane Theories
• On the Higgsing and UnHiggsing of Fano 3-Folds
• Quasi-Instantons and Supersymmetry Breaking
• Four-algebraic extension of the IIB matrix model
• Nambu variant of Local Resolution of Problem of Time and Background Independence
• On a generalization of Lie($k$): a CataLAnKe theorem
• Reynolds $n$-Lie algebras and NS-$n$-Lie algebras
• Mass-Deformed BLG Theory in Light-Cone Superspace
• Lie $3-$algebra and super-affinization of split-octonions
• Algebraic vs physical N=6 3-algebras
• Superconformal Chern-Simons theories beyond leading order
• Perturbative aspects of mass-deformed N=3 Chern-Simons-matter theory
• Multiple M-branes and 3-algebras
• Classification of linearly compact simple N=6 3-algebras
• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory
• Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
• On the Spectral properties of Multi-branes, M2 and M5 branes
• Moduli and BPS configurations of the BLG theory
• A simplified presentation of Specht modules
• Janus Field Theories from Non-Linear BF Theories for Multiple M2-Branes
• k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems
• 3d CFT and Multi M2-brane Theory on RxS^2
• Heterotic M2-branes
• Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-Lie algebras
• Mass Deformation of the Multiple M2 Branes Theory
• Unexpected Features of Supersymmetry with Central Charges
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• Embedding and partial resolution of complex cones over Fano threefolds
• Non-abelian D=11 Supermembrane
• Stability and rigidity of 3-Lie algebra morphisms
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Cohomologies of 3-Lie algebras with derivations
• Generalized representations of 3-Hom-Lie algebras
• Branes and Geometry in String and M-Theory
• Metric 3-Leibniz algebras and M2-branes
• Mass Deformed L-BLG Theory From ABJ Theory
• Hidden quartic symmetry in N=2 supersymmetry
• 3-Leibniz bialgebra in $N=6$ Chern-Simons gauge theories, multiple M2 to D2 branes and vice versa