14066902
Classification of the BPS states in Bagger-Lambert Theory
We classify, in a group theoretical manner, the BPS configura tions in the multiple M2-brane theory recently proposed by Bagger and Lambert. We present three types of BPS equations preserving various fractions of supersymmetries: in the first type we have const ant fields and the interactions are purely algebraic in nature; in the second type the equations are inv ariant under spatial rotation SO(2), and the fields can be time-dependent; in the third class the equat ions are invariant under boost SO(1;1) and provide the eleven-dimensional generalizations of the Nahm equations. The BPS equations for different number of supersymmetries exhibit the division a lgebra structures: octonion, quarternion or complex.
44214844
Abelian decomposition of Einstein's theory: Reformulation of general relativity
We propose a reformulation of general relativity by making the Abelian decomposition of Einstein's theory. Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein's gravitational connection (the gauge potential of Lorentz group $\vGm_\mu$) into the restricted connection made of the potential of the maximal Abelian subgroup $H$ of Lorentz group $G$ and the valence connection made of $G/H$ part of the potential which transforms covariantly under Lorentz group. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, because Lorentz group has two maximal Abelian subgroups. In this decomposition the role of the space-time metric $g_\mn$ is replaced by a four-index metric tensor $\vg_\mn$ which transforms covariantly under the Lorentz group, and the metric-compatibility condition $\nabla_\alpha g_\mn=0$ of the connection is replaced by the gauge covariant condition $D_\mu \vg^\mn$ which tells that $\vg_\mn$ is invariant under the parallel transport along the $\pro_\mu$-direction defined by $\vGm_\mu$. We discuss the physical implications of the Abelian decomposition. In particular, we argue that the decomposition implies the existence of a restricted theory of gravitation which has the full general invariance but has less physical degrees of freedom.
119097342
Torsion as a dynamic degree of freedom of quantum gravity
The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A?cd is developed. We consider SO(1, 3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum gravity. The torsion is proposed to represent a dynamic degree of freedom of quantum gravity at scales above the Planckian energy. The Einstein?Hilbert theory is induced as an effective theory due to quantum corrections of torsion via generating a stable gravito-magnetic condensate. We conjecture that torsion possesses an intrinsic quantum nature and can be confined.
118275742
Supersymmetry non-renormalization theorem from a computer and the AdS/CFT correspondence
We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which reduces the calculation to that of corresponding correlation functions in the plane-wave matrix model or the BMN matrix model. This model is a 1d gauge theory with 16 supersymmetries, which can be simulated in a manner similar to the recent studies of the D0-brane system. We study two-point and three-point functions of chiral primary operators at various coupling constant, and find that they agree with the free theory results up to overall constant factors. The ratio of the overall factors for two-point and three-point functions agrees with the prediction of the AdS/CFT correspondence.
118339519
5-dim superconformal index with enhanced En global symmetry
A bstractThe five-dimensional $ \mathcal{N}=1 $ supersymmetric gauge theory with Sp(N) gauge group and SO(2Nf) flavor symmetry describes the physics on N D4-branes with Nf D8-branes on top of a single O8 orientifold plane in Type I′ theory. This theory is known to be superconformal at the strong coupling limit with the enhanced global symmetry $ {E_{{N_f +1}}} $ for Nf ≤ 7. In this work we calculate the superconformal index on S1 × S4 for the Sp(1) gauge theory by the localization method and confirm such enhancement of the global symmetry at the superconformal limit for Nf ≤ 5 to a few leading orders in the chemical potential. Both perturbative and (anti)instanton contributions are present in this calculation. For Nf = 6, 7 cases some issues related the pole structure of the instanton calculation could not be resolved and here we could provide only some suggestive answer for the leading contributions to the index. For the Sp(N) case, similar issues related to the pole structure appear.
120898350
Surplus Solid Angle in Horava-Lifshitz Gravity
We consider Hořava-Lifshitz gravity coupled to the electrostatic field of a point charge, and show that the static solutions describe a space with a surplus (or deficit) solid angle. Unlike in general relativity, appearance of a surplus angle seems generic in Hořava-Lifshitz gravity. We discuss possible astrophysical effects due to a surplus angle.
118643039
GALAXY CLUSTERING TOPOLOGY IN THE SLOAN DIGITAL SKY SURVEY MAIN GALAXY SAMPLE: A TEST FOR GALAXY FORMATION MODELS
We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by Mr < ?20.19 enables us to measure the genus curve with an amplitude of G = 378 at 6 h ?1 Mpc smoothing scale, with 4.8% uncertainty including all systematics and cosmic variance. The clustering topology over the smoothing length interval from 6 to 10 h ?1 Mpc reveals a mild scale dependence for the shift (??) and void abundance (AV ) parameters of the genus curve. We find substantial bias in the topology of galaxy clustering with respect to the predicted topology of the matter distribution, which varies with luminosity, morphology, color, and the smoothing scale of the density field. The distribution of relatively brighter galaxies shows a greater prevalence of isolated clusters and more percolated voids. Even though early (late)-type galaxies show topology similar to that of red (blue) galaxies, the morphology dependence of topology is not identical to the color dependence. In particular, the void abundance parameter AV depends on morphology more strongly than on color. We test five galaxy assignment schemes applied to cosmological N-body simulations of a ?CDM universe to generate mock galaxies: the halo-galaxy one-to-one correspondence model, the halo occupation distribution model, and three implementations of semi-analytic models (SAMs). None of the models reproduces all aspects of the observed clustering topology; the deviations vary from one model to another but include statistically significant discrepancies in the abundance of isolated voids or isolated clusters and the amplitude and overall shift of the genus curve. SAM predictions of the topology color dependence are usually correct in sign but incorrect in magnitude. Our topology tests indicate that, in these models, voids should be emptier and more connected and the threshold for galaxy formation should be at lower densities.
119294901
E8(8) in Light Cone Superspace
We derive the non-linear action of E-8(8) on the constrained chiral superfield in the light-cone superspace with eight complex Grassmann variables. We construct (to lowest order in the coupling) the sixteen dynamical supersymmetries which generate a Hamiltonian with E-8(8) invariance in three space-time dimensions, and show that it has only interactions with even powers of the coupling constant.
5691719
Surplus Solid Angle: Toward Astrophysical Test of Horava-Lifshitz Gravity
We consider the electrostatic field of a point charge coupled to Hořava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Hořava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Hořava-Lifshitz gravity and obtain a series of exact solutions. © 2009 The American Physical Society.