34 research outputs found
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