228 research outputs found
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
The 1/N expansion of colored tensor models
In this paper we perform the 1/N expansion of the colored three dimensional
Boulatov tensor model. As in matrix models, we obtain a systematic topological
expansion, with more and more complicated topologies suppressed by higher and
higher powers of N. We compute the first orders of the expansion and prove that
only graphs corresponding to three spheres S^3 contribute to the leading order
in the large N limit.Comment: typos corrected, references update
Topological Graph Polynomials in Colored Group Field Theory
In this paper we analyze the open Feynman graphs of the Colored Group Field
Theory introduced in [arXiv:0907.2582]. We define the boundary graph
\cG_{\partial} of an open graph \cG and prove it is a cellular complex.
Using this structure we generalize the topological (Bollobas-Riordan) Tutte
polynomials associated to (ribbon) graphs to topological polynomials adapted to
Colored Group Field Theory graphs in arbitrary dimension
Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory
We show that the simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is
asymptotically safe to all orders in perturbation theor
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
Towards classical geometrodynamics from Group Field Theory hydrodynamics
We take the first steps towards identifying the hydrodynamics of group field
theories (GFTs) and relating this hydrodynamic regime to classical
geometrodynamics of continuum space. We apply to GFT mean field theory
techniques borrowed from the theory of Bose condensates, alongside standard GFT
and spin foam techniques. The mean field configuration we study is, in turn,
obtained from loop quantum gravity coherent states. We work in the context of
2d and 3d GFT models, in euclidean signature, both ordinary and colored, as
examples of a procedure that has a more general validity. We also extract the
effective dynamics of the system around the mean field configurations, and
discuss the role of GFT symmetries in going from microscopic to effective
dynamics. In the process, we obtain additional insights on the GFT formalism
itself.Comment: revtex4, 32 pages. Contribution submitted to the focus issue of the
New Journal of Physics on "Classical and Quantum Analogues for Gravitational
Phenomena and Related Effects", R. Schuetzhold, U. Leonhardt and C. Maia,
Eds; v2: typos corrected, references updated, to match the published versio
Classical Setting and Effective Dynamics for Spinfoam Cosmology
We explore how to extract effective dynamics from loop quantum gravity and
spinfoams truncated to a finite fixed graph, with the hope of modeling
symmetry-reduced gravitational systems. We particularize our study to the
2-vertex graph with N links. We describe the canonical data using the recent
formulation of the phase space in terms of spinors, and implement a
symmetry-reduction to the homogeneous and isotropic sector. From the canonical
point of view, we construct a consistent Hamiltonian for the model and discuss
its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the
dynamics from the spinfoam approach. We compute exactly the transition
amplitude between initial and final coherent spin networks states with support
on the 2-vertex graph, for the choice of the simplest two-complex (with a
single space-time vertex). The transition amplitude verifies an exact
differential equation that agrees with the Hamiltonian constructed previously.
Thus, in our simple setting we clarify the link between the canonical and the
covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made
explicit and emphasize
Laplacians on discrete and quantum geometries
We extend discrete calculus for arbitrary (-form) fields on embedded
lattices to abstract discrete geometries based on combinatorial complexes. We
then provide a general definition of discrete Laplacian using both the primal
cellular complex and its combinatorial dual. The precise implementation of
geometric volume factors is not unique and, comparing the definition with a
circumcentric and a barycentric dual, we argue that the latter is, in general,
more appropriate because it induces a Laplacian with more desirable properties.
We give the expression of the discrete Laplacian in several different sets of
geometric variables, suitable for computations in different quantum gravity
formalisms. Furthermore, we investigate the possibility of transforming from
position to momentum space for scalar fields, thus setting the stage for the
calculation of heat kernel and spectral dimension in discrete quantum
geometries.Comment: 43 pages, 2 multiple figures. v2: discussion improved, references
added, minor typos correcte
- …