M2-branes, 3-Lie algebras and Plucker relations

By Georgios Papadopoulos. 2008

280 citations recorded by the source corpus.

We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a (N) Lie algebra for N>2. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/61f44a5200283abb672c6ed3332dc50dc97a41b3

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Citations in the corpus

Constraining Maximally Supersymmetric Membrane Actions (2008, result): “Note added: Concurrent with the posting of this work to the ArXive, a proof of this result also appeared in [21].”
Nonabelian (2,0) tensor multiplets and 3-algebras (2010, background): “In particular there is exactly one [21, 22] Euclidean four-dimensional 3-algebra, A4, as well as an infinite set of Lorentzian 3-algebras [15–17].”
M5 from M2 (2008, background): “This was finally proved in [11, 12] very recently.”
Bagger-Lambert Theory for General Lie Algebras (2008, background): “In [7, 8] it has been proven that the only 3-algebras with a positive definite 3-algebra metric h are A4⊕.”
Charges of monopole operators in Chern-Simons Yang-Mills theory (2009, methodology): “Gustavsson [5] succeeded in constructing the ﬁrst N= 8 supersymmetric classical actions for Chern-Simons gauge ﬁelds coupled to matter. Requiring manifest unitarity restricts the gauge group to SO(4) [6,7]; this model may be reformulated as SU(2)×SU(2) gauge theory with conventional Chern-Simons ter”
M2 to D2 revisited (2008, result): “This conjecture was later proved in Refs. [ 17 ,18]. 1”
Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry (2008, background): “It wassuggested that the theory would be a gauge theory in whi h the gauge elds ou-ple to dimension-1/2 s alar and dimension-1 spinor elds.”
N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, background): “It can be however shown that the only possible 3-algebra is in fact SO(4) with fabcd = εabcd, once we suppose hab = tr(tatb) is positive definite [24, 25].”
On type IIA Penrose limit and = 6 Chern-Simons theories (2008, background): “If we assume the positive metric of the Lie 3-algebra, the algebra constraints the Lagrangian strongly [14, 18, 19, 20].”
Ghost-free superconformal action for multiple M2-branes (2008, background): “led to the discovery of a theory with SO(4) gauge symmetry [2]. Its full superconformal symmetry was veriﬁed in [6], which also conjectured its uniqueness. The uniqueness of this theory was proved in [7, 8]. A proposal for its physical interpretation in terms of M2-branes in M-theory at an M-fold si”
n-ary algebras: a review with applications (2010, methodology): “The fact that there is a unique simple(1) euclidean 3-Lie algebra (A4) was actually rediscovered in the context of the first BLG model, where it follows [34,35] by assuming that the metric needed for the BLG action has to be positive definite, a condition that may be relaxed.”