11 research outputs found
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
The 1/N expansion of colored tensor models in arbitrary dimension
In this paper we extend the 1/N expansion introduced in [1] to group field
theories in arbitrary dimension and prove that only graphs corresponding to
spheres S^D contribute to the leading order in the large N limit.Comment: 4 pages, 3 figure
Effective Hamiltonian Constraint from Group Field Theory
Spinfoam models provide a covariant formulation of the dynamics of loop
quantum gravity. They are non-perturbatively defined in the group field theory
(GFT) framework: the GFT partition function defines the sum of spinfoam
transition amplitudes over all possible (discretized) geometries and
topologies. The issue remains, however, of explicitly relating the specific
form of the group field theory action and the canonical Hamiltonian constraint.
Here, we suggest an avenue for addressing this issue. Our strategy is to expand
group field theories around non-trivial classical solutions and to interpret
the induced quadratic kinematical term as defining a Hamiltonian constraint on
the group field and thus on spin network wave functions. We apply our procedure
to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss
the relevance of understanding the spectrum of this Hamiltonian operator for
the renormalization of group field theories.Comment: 14 page
Bubbles and jackets: new scaling bounds in topological group field theories
We use a reformulation of topological group field theories in 3 and 4
dimensions in terms of variables associated to vertices, in 3d, and edges, in
4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4
dimensions, we obtain a bubble bound proving the suppression of singular
topologies with respect to the first terms in the perturbative expansion (in
the cut-off). We also prove a new, stronger jacket bound than the one currently
available in the literature. We expect these results to be relevant for other
tensorial field theories of this type, as well as for group field theory models
for 4d quantum gravity.Comment: v2: Minor modifications to match published versio
Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry
We deform the action and the supersymmetry transformations of the d = 10 and d = 4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d = 6 vector branes related to chiral (2,0) supergravity, which we denote as 'Vp-branes'. We use a space-filling V5 superbrane for the d = 6 model and a V3 superbrane for the d = 4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d = 10 and 4, and half-maximal 8+8 supersymmetries in d = 6 and 4.</p
The Spin Foam Approach to Quantum Gravity
This article reviews the present status of the spin foam approach to the
quantization of gravity. Special attention is payed to the pedagogical
presentation of the recently introduced new models for four dimensional quantum
gravity. The models are motivated by a suitable implementation of the path
integral quantization of the Plebanski formulation of gravity on a simplicial
regularization. The article also includes a self-contained treatment of the 2+1
gravity. The simple nature of the latter provides the basis and a perspective
for the analysis of both conceptual and technical issues that remain open in
four dimensions.Comment: To appear in Living Reviews in Relativit