33 research outputs found
EPRL/FK Group Field Theory
The purpose of this short note is to clarify the Group Field Theory vertex
and propagators corresponding to the EPRL/FK spin foam models and to detail the
subtraction of leading divergences of the model.Comment: 20 pages, 2 figure
Two and four-loop -functions of rank 4 renormalizable tensor field theories
A recent rank 4 tensor field model generating 4D simplicial manifolds has
been proved to be renormalizable at all orders of perturbation theory
[arXiv:1111.4997 [hep-th]]. The model is built out of
(), () interactions and an anomalous
term (). The -functions of this model are evaluated at two
and four loops. We find that the model is asymptotically free in the UV for
both the main interactions whereas it is safe in the
sector. The remaining anomalous term turns out to possess a
Landau ghost.Comment: 31 pages, 31 figures; improved versio
Functional renormalisation group approach for tensorial group field theory: a rank-3 model
Renormalization of the commutative scalar theory with harmonic term to all orders
The noncommutative scalar theory with harmonic term (on the Moyal space) has
a vanishing beta function. In this paper, we prove the renormalizability of the
commutative scalar field theory with harmonic term to all orders by using
multiscale analysis in the momentum space. Then, we consider and compute its
one-loop beta function, as well as the one on the degenerate Moyal space. We
can finally compare both to the vanishing beta function of the theory with
harmonic term on the Moyal space.Comment: 16 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
Physical states in the canonical tensor model from the perspective of random tensor networks
Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
A dual formulation of group field theories, obtained by a Fourier transform
mapping functions on a group to functions on its Lie algebra, has been proposed
recently. In the case of the Ooguri model for SO(4) BF theory, the variables of
the dual field variables are thus so(4) bivectors, which have a direct
interpretation as the discrete B variables. Here we study a modification of the
model by means of a constraint operator implementing the simplicity of the
bivectors, in such a way that projected fields describe metric tetrahedra. This
involves a extension of the usual GFT framework, where boundary operators are
labelled by projected spin network states. By construction, the Feynman
amplitudes are simplicial path integrals for constrained BF theory. We show
that the spin foam formulation of these amplitudes corresponds to a variant of
the Barrett-Crane model for quantum gravity. We then re-examin the arguments
against the Barrett-Crane model(s), in light of our construction.Comment: revtex, 24 page