161 research outputs found
Renormalization of noncommutative phi 4-theory by multi-scale analysis
In this paper we give a much more efficient proof that the real Euclidean phi
4-model on the four-dimensional Moyal plane is renormalizable to all orders. We
prove rigorous bounds on the propagator which complete the previous
renormalization proof based on renormalization group equations for non-local
matrix models. On the other hand, our bounds permit a powerful multi-scale
analysis of the resulting ribbon graphs. Here, the dual graphs play a
particular r\^ole because the angular momentum conservation is conveniently
represented in the dual picture. Choosing a spanning tree in the dual graph
according to the scale attribution, we prove that the summation over the loop
angular momenta can be performed at no cost so that the power-counting is
reduced to the balance of the number of propagators versus the number of
completely inner vertices in subgraphs of the dual graph.Comment: 34 page
Two and Three Loops Beta Function of Non Commutative Theory
The simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is asymptotically
safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this
result up to three loops. If this remains true at any loop, it should allow a
full non perturbative construction of this model.Comment: 24 pages, 7 figure
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
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
One-loop functions of a translation-invariant renormalizable noncommutative scalar model
Recently, a new type of renormalizable scalar model on
the Moyal space was proved to be perturbatively renormalizable. It is
translation-invariant and introduces in the action a term. We
calculate here the and functions at one-loop level for this
model. The coupling constant function is proved to have the
same behaviour as the one of the model on the commutative
. The function of the new parameter is also
calculated. Some interpretation of these results are done.Comment: 13 pages, 3 figure
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
Overview of the parametric representation of renormalizable non-commutative field theory
We review here the parametric representation of Feynman amplitudes of
renormalizable non-commutative quantum field models.Comment: 10 pages, 3 figures, to be published in "Journal of Physics:
Conference Series
Commutative limit of a renormalizable noncommutative model
Renormalizable models on Moyal space have been obtained by
modifying the commutative propagator. But these models have a divergent "naive"
commutative limit. We explain here how to obtain a coherent such commutative
limit for a recently proposed translation-invariant model. The mechanism relies
on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte
Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
Based on recent work on simplicial diffeomorphisms in colored group field
theories, we develop a representation of the colored Boulatov model, in which
the GFT fields depend on variables associated to vertices of the associated
simplicial complex, as opposed to edges. On top of simplifying the action of
diffeomorphisms, the main advantage of this representation is that the GFT
Feynman graphs have a different stranded structure, which allows a direct
identification of subgraphs associated to bubbles, and their evaluation is
simplified drastically. As a first important application of this formulation,
we derive new scaling bounds for the regularized amplitudes, organized in terms
of the genera of the bubbles, and show how the pseudo-manifolds configurations
appearing in the perturbative expansion are suppressed as compared to
manifolds. Moreover, these bounds are proved to be optimal.Comment: 28 pages, 17 figures. Few typos fixed. Minor corrections in figure 6
and theorem
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