Constraining Maximally Supersymmetric Membrane Actions

By J. Gauntlett, J. Gutowski. 2008

234 citations recorded by the source corpus.

We study the recent construction of maximally supersymmetric field theory Lagrangians in three spacetime dimensions that are based on algebras with a triple product. Assuming that the algebra has a positive definite metric compatible with the triple product, we prove that the only non-trivial examples are either the well known case based on a four dimensional algebra or direct sums thereof.

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

View Paper: https://www.semanticscholar.org/paper/c3e21187f7604a00e0f96df0864025b0d057f46c

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Citations in the corpus

M2 to D2 revisited (2008, result): “This conjecture was later proved in Refs. [17, 18 ]. 1”
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].”
M5-brane in three-form flux and multiple M2-branes (2008, background): “can be reduced to the direct sum of A4 [23].”
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): “The uniqueness of this theory was proved in [7, 8 ]. A pro-”
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].”
n-ary algebras: a review with applications (2010, background): “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.”
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⊕.”
M5 from M2 (2008, background): “This was finally proved in [11, 12] very recently.”
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”
Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry (2008, background): “The BLG theory was conjectured [23] and proved [25, 26 ] to be the unique theory of this type with maximal supersymmetry.”