On Non Commutative G2 structure

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras. We show that there are eight possible solutions for this extended structure, one of which corresponds to the commutative case. Then we obtain a matrix representation solving such algebras using combinatorial arguments. An application to matrix model of M-theory is discussed.Comment: 16 pages, Latex. Typos corrected, minor changes. Version to appear in J. Phys.A: Math.Gen.(2005

Remarks on the Scalar Graviton Decoupling and Consistency of Horava Gravity

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. But there have been confusions regarding the extra scalar graviton mode and the consistency of the Horava model. I reconsider these problems and show that, in the Minkowski vacuum background, the scalar graviton mode can be consistency decoupled from the usual tensor graviton modes by imposing the (local) Hamiltonian as well as the momentum constraints.Comment: Some clarifications regarding the projectable case added, Typos corrected, Comments (Footnote No.9, Note Added) added, References updated, Accepted in CQ

Global monopole solutions in Horava gravity

In Horava's theory of gravity coupled to a global monopole source, we seek for static, spherically symmetric spacetime solutions for general values of $\lambda$. We obtain the explicit solutions with deficit solid angles, in the IR modified Horava gravity model, at the IR fixed point $\lambda=1$ and at the conformal point $\lambda=1/3$. For the other values of $1>\lambda>0$ we also find special solutions to the inhomogenous equation of the gravity model with detailed balance, and we discuss an possibility of astrophysical applications of the $\lambda=1/2$ solution that has a deficit angle for a finite range.Comment: 7 pages, added reference

Non-abelian D=11 Supermembrane

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes.Comment: Contribution to the Proceedings of the Dubna International SQS'09 Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3, 2009. 12pg, Late

Black Holes in Ho\v{r}ava Gravity with Higher Derivative Magnetic Terms

We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the near-extremal limit, for asymptotically flat and (anti-)de Sitter spaces. We also construct a detailed balanced version of the theory, for which we find projectable and non-projectable, non-perturbative solutions.Comment: 17 pages. v2: Up to date with published version; some minor remarks and more reference