## 23 Citations

### LIE 3-ALGEBRA AND SUPER-AFFINIZATION OF SPLIT-OCTONIONS

- Mathematics
- 2011

The purpose of this study is to extend the concept of a generalized Lie 3-algebra, known to the divisional algebra of the octonions 𝕆, to split-octonions 𝕊𝕆, which is non-divisional. This is…

### A new three-algebra representation for the Superconformal Chern-Simons Theory

- Mathematics
- 2008

Based on the realization of three-algebras in terms of algebra of matrices and four-brackets [arXiv:0807.1570] we present the notion of u(N)-based extended threealgebras, which for N = 2 reproduces…

### Squashing gravity dual of superconformal Chern–Simons gauge theory

- Physics
- 2009

Four-dimensional field equations are determined for perturbations of the quotient 7-sphere size and squashing parameter in 11-dimensional supergravity. The quotient 7-sphere is an S1-bundle over the…

### On the Lie-Algebraic Origin of Metric 3-Algebras

- Mathematics
- 2009

Since the pioneering work of Bagger–Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern–Simons theories whose main ingredient is a metric 3-algebra. On…

### Metric 3-Leibniz algebras and M2-branes

- Mathematics
- 2010

This thesis is concerned with superconformal Chern-Simons theories with matter in 3 dimensions. The interest in these theories is two-fold. On the one hand, it is a new family of theories in which to…

### M2-brane flows and the Chern-Simons level

- Mathematics
- 2009

The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the dual geometry. This suggests that if we move the membranes away from the tip of the orbifold to a smooth point, it should…

### Exceptional Jordan Strings/Membranes and Octonionic Gravity/p-branes

- Mathematics
- 2011

Nonassociative Octonionic Ternary Gauge Field Theories are revisited paving the path to an analysis of the many physical applications of Exceptional Jordan Strings/Membranes and Octonionic Gravity.…

### Freudenthal Gauge Theory

- Mathematics
- 2013

A bstractWe present a novel gauge field theory, based on the Freudenthal Triple System (FTS), a ternary algebra with mixed symmetry (not completely symmetric) structure constants. The theory, named…

### Octonionic Ternary Gauge Field Theories Revisited

- Mathematics
- 2013

An octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket defined earlier by Yamazaki. The ternary infinitesimal gauge transformations do obey the key $closure$…

### A non-associative quaternion scalar ﬁeld theory

- Mathematics
- 2013

A non-associative Groenewold-Moyal plane is constructed using quaternion-valued function algebras. The symmetrized multi-particle states, the scalar product, the annihilation/creation algebra and the…

## References

SHOWING 1-10 OF 52 REFERENCES

### M2-branes, 3-Lie algebras and Plucker relations

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Physics, Mathematics
- 2008

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

- Mathematics
- 2009

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.

- MathematicsPhysical review letters
- 2008

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

- Physics, Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics, Physics
- 2008

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…