176 research outputs found
Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
We offer a perspective on some recent results obtained in the context of the
group field theory approach to quantum gravity, on top of reviewing them
briefly. These concern a natural mechanism for the emergence of non-commutative
field theories for matter directly from the GFT action, in both 3 and 4
dimensions and in both Riemannian and Lorentzian signatures. As such they
represent an important step, we argue, in bridging the gap between a quantum,
discrete picture of a pre-geometric spacetime and the effective continuum
geometric physics of gravity and matter, using ideas and tools from field
theory and condensed matter analog gravity models, applied directly at the GFT
level.Comment: 13 pages, no figures; uses JPConf style; contribution to the
proceedings of the D.I.C.E. 2008 worksho
A quantum field theory of simplicial geometry and the emergence of spacetime
We present the case for a fundamentally discrete quantum spacetime and for
Group Field Theories as a candidate consistent description of it, briefly
reviewing the key properties of the GFT formalism. We then argue that the
outstanding problem of the emergence of a continuum spacetime and of General
Relativity from fundamentally discrete quantum structures should be tackled
from a condensed matter perspective and using purely QFT methods, adapted to
the GFT context. We outline the picture of continuum spacetime as a condensed
phase of a GFT and a research programme aimed at realizing this picture in
concrete terms.Comment: 10 pages, no figures; to appear in the Proceedings of the DICE 2006
Workshop (Piombino, Italy), uses IOP Conf style; v2: typos corrected, added
preprint number
From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model
A Kaluza-Klein like approach for a 4d spin foam model is considered. By
applying this approach to a model based on group field theory in 4d (TOCY
model), and using the Peter-Weyl expansion of the gravitational field,
reconstruction of new non gravitational fields and interactions in the action
are found. The perturbative expansion of the partition function produces graphs
colored with su(2) algebraic data, from which one can reconstruct a 3d
simplicial complex representing space-time and its geometry; (like in the
Ponzano-Regge formulation of pure 3d quantum gravity), as well as the Feynman
graph for typical matter fields. Thus a mechanism for generation of matter and
construction of new dimensions are found from pure gravity.Comment: 11 pages, no figure, to be published in International Journal of
Geometric Methods in Modern Physic
Dynamics of anisotropies close to a cosmological bounce in quantum gravity
We study the dynamics of perturbations representing deviations from perfect
isotropy in the context of the emergent cosmology obtained from the group field
theory formalism for quantum gravity. Working in the mean field approximation
of the group field theory formulation of the Lorentzian EPRL model, we derive
the equations of motion for such perturbations to first order. We then study
these equations around a specific simple isotropic background, characterised by
the fundamental representation of \mbox{SU(2)}, and in the regime of the
effective cosmological dynamics corresponding to the bouncing region replacing
the classical singularity, well approximated by the free GFT dynamics. In this
particular example, we identify a region in the parameter space of the model
such that perturbations can be large at the bounce but become negligible away
from it, i.e. when the background enters the non-linear regime. We also study
the departures from perfect isotropy by introducing specific quantities, such
as the surface-area-to-volume ratio and the effective volume per quantum, which
make them quantitative.Comment: 45 pages, 4 figure
Group field theory renormalization - the 3d case: power counting of divergences
We take the first steps in a systematic study of Group Field Theory
renormalization, focusing on the Boulatov model for 3D quantum gravity. We
define an algorithm for constructing the 2D triangulations that characterize
the boundary of the 3D bubbles, where divergences are located, of an arbitrary
3D GFT Feynman diagram. We then identify a special class of graphs for which a
complete contraction procedure is possible, and prove, for these, a complete
power counting. These results represent important progress towards
understanding the origin of the continuum and manifold-like appearance of
quantum spacetime at low energies, and of its topology, in a GFT framework
Random tensor models in the large N limit: Uncoloring the colored tensor models
Tensor models generalize random matrix models in yielding a theory of
dynamical triangulations in arbitrary dimensions. Colored tensor models have
been shown to admit a 1/N expansion and a continuum limit accessible
analytically. In this paper we prove that these results extend to the most
general tensor model for a single generic, i.e. non-symmetric, complex tensor.
Colors appear in this setting as a canonical book-keeping device and not as a
fundamental feature. In the large N limit, we exhibit a set of Virasoro
constraints satisfied by the free energy and an infinite family of
multicritical behaviors with entropy exponents \gamma_m=1-1/m.Comment: 15 page
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
Group field theory formulation of 3d quantum gravity coupled to matter fields
We present a new group field theory describing 3d Riemannian quantum gravity
coupled to matter fields for any choice of spin and mass. The perturbative
expansion of the partition function produces fat graphs colored with SU(2)
algebraic data, from which one can reconstruct at once a 3-dimensional
simplicial complex representing spacetime and its geometry, like in the
Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs
for the matter fields. The model then assigns quantum amplitudes to these fat
graphs given by spin foam models for gravity coupled to interacting massive
spinning point particles, whose properties we discuss.Comment: RevTeX; 28 pages, 21 figure
The Complete Barrett-Crane Model and its Causal Structure
The causal structure is a quintessential element of continuum spacetime
physics and needs to be properly encoded in a theory of Lorentzian quantum
gravity. Established spin foam (and tensorial group field theory (TGFT)) models
mostly work with relatively special classes of Lorentzian triangulations (e.g.
built from spacelike tetrahedra only), obscuring the explicit implementation of
the local causal structure at the microscopic level. We overcome this
limitation and construct a full-fledged model for Lorentzian quantum geometry
the building blocks of which include spacelike, lightlike and timelike
tetrahedra. We realize this within the context of the Barrett-Crane TGFT model.
Following an explicit characterization of the amplitudes via methods of
integral geometry, and the ensuing clear identification of local causal
structure, we analyze the model's amplitudes with respect to its
(space)time-orientation properties and provide also a more detailed comparison
with the framework of causal dynamical triangulations (CDT).Comment: 40 + 14 pages, 7 figure
Emergent cosmology from quantum gravity in the Lorentzian Barrett-Crane tensorial group field theory model
We study the cosmological sector of the Lorentzian Barrett-Crane (BC) model coupled to a free massless scalar field in its Group Field Theory (GFT) formulation, corresponding to the mean-field hydrodynamics obtained from coherent condensate states. The relational evolution of the condensate with respect to the scalar field yields effective dynamics of homogeneous and isotropic cosmologies, similar to those previously obtained in SU(2)-based EPRL-like models. Also in this manifestly Lorentzian setting, in which only continuous SL(2,Bbb C)-representations are used, we obtain generalized Friedmann equations that generically exhibit a quantum bounce, and can reproduce all of the features of the cosmological dynamics of EPRL-like models. This lends support to the expectation that the EPRL-like and BC models may lie in the same continuum universality class, and that the quantum gravity mechanism producing effective bouncing scenarios may not depend directly on the discretization of geometric observables
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