Canonical Analysis of Algebraic String Actions

We investigate the canonical aspects of the algebraic first order formulation of strings introduced two decades ago by Balachandran and collaborators. We slightly enlarge the Lagrangian framework and show the existence of a self-dual formulation and of an Immirzi-type parameter reminiscent of four-dimensional first order gravity. We perform a full Hamiltonian analysis of the self-dual case: we extract the first class constraints and construct the Dirac bracket associated to the second class constraints. The first class constraints contain the diffeomorphisms algebra on the world-sheet, and the coordinates are shown to be non-commutative with respect to the Dirac bracket. The Hamilton equations in a particular gauge are shown to reproduce the wave equation for the string coordinates. In the general, non-self-dual case, we also explicit the first class constraints of the system and show that, unlike the self-dual formulation, the theory admits an extra propagating degree of freedom than the two degrees of freedom of conventional string theory. This prevents the general algebraic string from being strictly equivalent to the Nambu-Goto string.Comment: Title changed. Presentation improved. Typos correcte

On gravitational defects, particles and strings

We study the inclusion of point and string matter in the deSitter gauge theory, or MacDowell-Mansouri formulation of four dimensional gravity. We proceed by locally breaking the gauge symmetries of general relativity along worldlines and worldsheets embedded in the spacetime manifold. Restoring full gauge invariance introduces new dynamical fields which describe the dynamics of spinning matter coupled to gravity. We discuss the physical interpretation of the obtained formalism by studying the flat limit and the spinless case on arbitrary backgrounds. It turns out that the worldline action describes a massive spinning particle, while the worldsheet action contains the Nambu-Goto string augmented with spinning contributions. Finally, we study the gravity/matter variational problem and conclude by discussing potential applications of the formalism to the inclusion of the Nambu-Goto string in spinfoam models of four dimensional quantum gravity.Comment: 30 pages, no figure

q-Deformation of Lorentzian spin foam models

We construct and analyse a quantum deformation of the Lorentzian EPRL model. The model is based on the representation theory of the quantum Lorentz group with real deformation parameter. We give a definition of the quantum EPRL intertwiner, study its convergence and braiding properties and construct an amplitude for the four-simplexes. We find that the resulting model is finite.Comment: 12 pages, 2 figures, Proceedings of the 3rd Quantum Gravity and Quantum Geometry School (Zakopane, 2011), to appear in Po

Extended matter coupled to BF theory

Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions leading to an interpretation of the theory in terms of strings propagating on a flat spacetime. We also show that the general classical solutions of the theory are in one-to-one correspondence with solutions of Einstein's equations in the presence of distributional matter (cosmic strings). Secondly, we quantize the theory and present, in particular, a prescription to regularize the physical inner product of the canonical theory. We show how the resulting transition amplitudes are dual to evaluations of Feynman diagrams coupled to three-dimensional quantum gravity. Finally, we remove the regulator by proving the topological invariance of the transition amplitudes.Comment: 27 pages, 7 figure

Asymptotic analysis of the EPRL four-simplex amplitude

The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-simplex geometry, the asymptotic formula contains the Regge action for general relativity. A canonical choice of phase for the boundary state is introduced and is shown to be necessary to obtain the results.Comment: v2: improved presentation, typos corrected, refs added; results unchange

A Summary of the asymptotic analysis for the EPRL amplitude

We review the basic steps in building the asymptotic analysis of the Euclidean sector of new spin foam models using coherent states, for Immirzi parameter less than one. We focus on conceptual issues and by so doing omit peripheral proofs and the original discussion on spin structures.Comment: 8pages, Proceedings for Planck Scale 2009, talk given by Henrique Gome

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

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