An Invariant Action for Noncommutative Gravity in Four-Dimensions

Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to $U(1,1)\times U(1,1).$ No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.Comment: 11 pages. Paper shortened. Consideration is now limited to gravity in four-dimension

Mass Spectrum of D=11 Supergravity on AdS2 x S2 x T7

We compute the Kaluza-Klein mass spectrum of the D=11 supergravity compactified on AdS2 x S2 x T7 and arrange it into representations of the SU(1,1|2) superconformal algebra. This geometry arises in M theory as the near horizon limit of a D=4 extremal black-hole constructed by wrapping four groups of M-branes along the T7. Via AdS/CFT correspondence, our result gives a prediction for the spectrum of the chiral primary operators in the dual conformal quantum mechanics yet to be formulated.Comment: 30 pages, 2 figures; v3. more careful treatments of the boundary modes, and other minor correction

Stabilized Quantum Gravity: Stochastic Interpretation and Numerical Simulation

Following the reasoning of Claudson and Halpern, it is shown that "fifth-time" stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbitrary, initial and final states. The simple restriction to a fixed final state at $t_5 \rightarrow \infty$ is sufficient to stabilize the theory. This equivalence fixes the integration measure, and suggests a particular operator-ordering, for the fifth-time action of quantum gravity. Results of a numerical simulation of stabilized, latticized Einstein-Cartan theory on some small lattices are reported. In the range of cosmological constant \l investigated, it is found that: 1) the system is always in the broken phase $\ne 0$; and 2) the negative free energy is large, possibly singular, in the vincinity of \l = 0. The second finding may be relevant to the cosmological constant problem.Comment: 22 pages, 3 figures (now included as a postscript file

Noncommutative deformation of four dimensional Einstein gravity

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.Comment: LaTex, 11 pages, comments added, to appear in Classical and Quantum Gravit

Variable rest masses in 5-dimensional gravitation confronted with experimental data

Cosmological solutions of Einstein equation for a \mbox{5-dimensional} space-time, in the case of a dust-filled universe, are presented. With these solutions we are able to test a hypothetical relation between the rest mass of a particle and the $5^{\rm th}$ dimension. Comparison with experiment strongly refutes the implied dependence of the rest mass on the cosmological time.Comment: Some references adde

Calculation of Graviton Scattering Amplitudes using String-Based Methods

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.Comment: 25 pages +5 figs. , SWAT-94-37 UCLA/TEP/94/30, Plain TeX. (Typos in eqns. fixed

Canonical Quantum Supergravity in Three Dimensions, (some lines lost during submission)

We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on $N=2$ supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are found to be absent due to local supersymmetry. We show that the supersymmetry constraints can be partially solved by a functional analog of the method of characteristics. We also consider extensions of Wilson loop integrals of the type previously found in ordinary gravity, but now with connections involving the bosonic and fermionic matter fields in addition to the gravitational connection. In a separate section of this paper, the canonical treatment and quantization of non-linear coset space sigma models are discussed in a self contained way.Comment: 40 pages, LaTeX, DESY 93-07

Supercurrents in Matrix theory and the generalized AdS/CFT correspondence

We investigate Matrix theory in the large-N limit following the conjectured correspondence between Matrix theory and supergravity on the near-horizon limit of the D0-brane background. We analyze the complete fermionic spectrum of supergravity and obtain two-point functions of the supercurrents in Matrix theory. By examining the large-N scaling properties of the correlators, we discuss the consistency of the 11-dimensional interpretation of the supersymmetry of Matrix theory.Comment: 31 pages, Latex; Typos corrected, references added, final version to be published in Nucl.Phys.

Vertex Operators for Closed Superstrings

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic background in presence of Ramond-Ramond (RR) fields. We extend the procedure to all massive states of open and closed superstrings and we identify two new nilpotent charges which are used to impose the gauge fixing on the physical states. We solve iteratively the equations of the vertex for linear x-dependent RR field strengths. This vertex plays a role in studying non-constant C-deformations of superspace. Finally, we construct an action for the free massless sector of closed strings, and we propose a form for the kinetic term for closed string field theory in the pure spinor formalism.Comment: TeX, harvmac, amssym.tex, 41 pp; references adde

Construction of an SO(10) x U(1)_F Model of the Yukawa Interactions

We construct a supersymmetric $SO(10) \times U(1)_F$ model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The $U(1)_F$ family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the $SO(10)$ symmetry relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the $U(1)_F$ family symmetry to a small set of tree diagrams, and mainly complex-symmetric. The tree diagrams for the Majorana mass matrix are all non-renormalizable and of progressively higher-order, leading to a nearly geometrical structure. Pairs of ${\bf 1, 45, 10}$ and ${\bf 126}$ Higgs representations enter with those having large vacuum expectation values breaking the symmetry down to $SU(3)_c \times SU(2)_L \times U(1)_Y$ near the grand unification scale. In terms of 12 parameters expressed as the Yukawa couplings times vacuum expectation values for the Higgs representations employed, a realistic set of 15 quark and lepton masses (including those for the 3 heavy righthanded Majorana neutrinos) and 8 mixing parameters emerges for the neutrino scenario involving the non-adiabatic conversion of solar neutrinos and the depletion of atmospheric muon-neutrinos through oscillations into tau-neutrinos.Comment: 32 pages, latex with style files attached, 1 figure in uuencoded postscript fil