Three-algebras and N=6 Chern-Simons gauge theories

By J. Bagger, N. Lambert. 2008

325 citations recorded by the source corpus.

We derive the general form for a three-dimensional scale-invariant field theory with $\mathcal{N}=6$ 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 $\mathcal{N}=6$ theories that have been recently proposed as models for M2-branes in an ${\mathbb{R}}^{8}/{\mathbb{Z}}_{k}$ orbifold background.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e971e810da18a5cb798ffce6e978d2044326e47e

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Citations in the corpus

Generalized conformal symmetry and recovery of SO(8) in multiple M2 and D2 branes (2008, background): “In the formulation the 3-algebraic structure does not seem to play any role, but recently Bagger and Lambert showed that if the condition of the antisymmetry of the structure constant is relaxed, the ABJM theory can be written in terms of the new 3-algebra [19].”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “2 The supersymmetries of this action have been checked carefully in [8, 9], while its relation to the construction in terms of three-algebras has been described in [10, 11].”
Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry (2008, background): “The actions and supersymmetry transformations that are derived in [11, 13 ] appear to be equivalent to the actions and supersymmetry transformations that are obtained in this paper (without reference to 3-algebras).”
n-ary algebras: a review with applications (2010, background): “The Bagger-Lambert-Gustavsson (BLG) model We now come to the last part of this review, the appearance of 3-Lie and Nambu FA structures in brane theory.”
A Massive Study of M2-brane Proposals (2008, background): “It may also be written as a three-algebra theory with complex structure constants [38].”