3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.Comment: 17 pages, revtex4, 1 figur

Euclidean three-point function in loop and perturbative gravity

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of gamma<1. We find results consistent with Regge calculus in the limit gamma->0 and j->infinity. We also compute the tree-level three-point function of perturbative quantum general relativity in position space, and discuss the possibility of directly comparing the two results.Comment: 16 page

Coupling gauge theory to spinfoam 3d quantum gravity

We construct a spinfoam model for Yang-Mills theory coupled to quantum gravity in three dimensional riemannian spacetime. We define the partition function of the coupled system as a power series in g_0^2 G that can be evaluated order by order using grasping rules and the recoupling theory. With respect to previous attempts in the literature, this model assigns the dynamical variables of gravity and Yang-Mills theory to the same simplices of the spinfoam, and it thus provides transition amplitudes for the spin network states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly that the partition function has a semiclassical limit given by the Regge discretization of the classical Yang-Mills action.Comment: 18 page

Observables in 3d spinfoam quantum gravity with fermions

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.Comment: 32 pages, many diagrams, uses psfrag

Spin foams with timelike surfaces

Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3--vectors which represent normals to surfaces and lie either in the 2--sphere or the 2d hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint.Comment: 22 pages, no figures; v2: remarks on operator formalism added in discussion; correction: the spin 1/2 irrep of the discrete series does not appear in the Plancherel decompositio

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references adde

A new look at loop quantum gravity

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.Comment: 15 pages, 5 figure

Limit on the mass of a long-lived or stable gluino

We reinterpret the generic CDF charged massive particle limit to obtain a limit on the mass of a stable or long-lived gluino. Various sources of uncertainty are examined. The $R$-hadron spectrum and scattering cross sections are modeled based on known low-energy hadron physics and the resultant uncertainties are quantified and found to be small compared to uncertainties from the scale dependence of the NLO pQCD production cross sections. The largest uncertainty in the limit comes from the unknown squark mass: when the squark -- gluino mass splitting is small, we obtain a gluino mass limit of 407 GeV, while in the limit of heavy squarks the gluino mass limit is 397 GeV. For arbitrary (degenerate) squark masses, we obtain a lower limit of 322 GeV on the gluino mass. These limits apply for any gluino lifetime longer than $\sim 30$ ns, and are the most stringent limits for such a long-lived or stable gluino.Comment: 15 pages, 5 figures, accepted for publication in JHE

Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model

We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.Comment: 18 pages, 1 figur

Expansion history and f(R) modified gravity

We attempt to fit cosmological data using $f(R)$ modified Lagrangians containing inverse powers of the Ricci scalar varied with respect to the metric. While we can fit the supernova data well, we confirm the $a\propto t^{1/2}$ behaviour at medium to high redshifts reported elsewhere and argue that the easiest way to show that this class of models are inconsistent with the data is by considering the thickness of the last scattering surface. For the best fit parameters to the supernova data, the simplest 1/R model gives rise to a last scattering surface of thickness $\Delta z\sim 530$, inconsistent with observations.Comment: accepted in JCAP, presentation clarified, results and conclusions unchange