Octonions, G(2) and generalized Lie 3-algebras

@article{Yamazaki2008OctonionsGA,
  title={Octonions, G(2) and generalized Lie 3-algebras},
  author={Masahito Yamazaki},
  journal={Physics Letters B},
  year={2008},
  volume={670},
  pages={215-219}
}
  • M. Yamazaki
  • Published 10 September 2008
  • Mathematics
  • Physics Letters B
View PDF on arXiv
23 Citations
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23 Citations

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References

SHOWING 1-10 OF 52 REFERENCES

M2-branes, 3-Lie algebras and Plucker relations

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…

Multiple M2-branes and generalized 3-Lie algebras

We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in…

Superconformal M2-branes and generalized Jordan triple systems

Three-dimensional conformal theories with six supersymmetries and SU(4)R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the…

The superconformal gaugings in three dimensions

We show how three-dimensional superconformal theories for any number N ≤ 8 of supersymmetries can be obtained by taking a conformal limit of the corresponding three-dimensional gauged supergravity…

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

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…

Membranes on an orbifold.

An M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry is provided to describe two membranes moving in the orbifold R8/Z2.

The Superconformal Gauge Theory on M2-Branes

We show that by adding a supersymmetric Faddeev-Popov ghost sector to the recently constructed Bagger-Lambert theory based on a Lorentzian three algebra, we obtain an action with a BRST symmetry that…

Ghost-free superconformal action for multiple M2-branes

The Bagger-Lambert construction of Script N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary…

Tilings, Chern-Simons Theories and M2 Branes

A new infinite class of Chern-Simons theories in 2+1 dimensions is presented using brane tilings. The new class reproduces all known cases so far and introduces many new models that are dual to M2…

Supersymmetric Yang-Mills theory from lorentzian three-algebras

We show that by adding a supersymmetric Faddeev-Popov ghost sector to the recently constructed Bagger-Lambert theory based on a Lorentzian three algebra, we obtain an action with a BRST symmetry that…
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