27 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
Bipartite partial duals and circuits in medial graphs
It is well known that a plane graph is Eulerian if and only if its geometric
dual is bipartite. We extend this result to partial duals of plane graphs. We
then characterize all bipartite partial duals of a plane graph in terms of
oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric
Generalization of the Bollob\'as-Riordan polynomial for tensor graphs
Tensor models are used nowadays for implementing a fundamental theory of
quantum gravity. We define here a polynomial encoding the
supplementary topological information. This polynomial is a natural
generalization of the Bollob\'as-Riordan polynomial (used to characterize
matrix graphs) and is different of the Gur\uau polynomial, (R. Gur\uau,
"Topological Graph Polynomials in Colored Group Field Theory", Annales Henri
Poincare {\bf 11}, 565-584 (2010)) defined for a particular class of tensor
graphs, the colorable ones. The polynomial is defined for both
colorable and non-colorable graphs and it is proved to satisfy the
contraction/deletion relation. A non-trivial example of a non-colorable graphs
is analyzed.Comment: 22 pages, 20 figure
On the Effective Action of Noncommutative Yang-Mills Theory
We compute here the Yang-Mills effective action on Moyal space by integrating
over the scalar fields in a noncommutative scalar field theory with harmonic
term, minimally coupled to an external gauge potential. We also explain the
special regularisation scheme chosen here and give some links to the Schwinger
parametric representation. Finally, we discuss the results obtained: a
noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference
on Noncommutative Geometry and Physics", April 2007, Orsay (France). To
appear in J. Phys. Conf. Se
One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
We compute at the one-loop order the beta-functions for a renormalisable
non-commutative analog of the Gross Neveu model defined on the Moyal plane. The
calculation is performed within the so called x-space formalism. We find that
this non-commutative field theory exhibits asymptotic freedom for any number of
colors. The beta-function for the non-commutative counterpart of the Thirring
model is found to be non vanishing.Comment: 16 pages, 9 figure
Degenerate noncommutativity
We study a renormalizable four dimensional model with two deformed quantized
space directions. A one-loop renormalization is performed explicitly. The
Euclidean model is connected to the Minkowski version via an analytic
continuation. At a special value of the parameters a nontrivial fixed point of
the renormalization group occurs.Comment: 16 page
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
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
Vacuum configurations for renormalizable non-commutative scalar models
In this paper we find non-trivial vacuum states for the renormalizable
non-commutative model. An associated linear sigma model is then
considered. We further investigate the corresponding spontaneous symmetry
breaking.Comment: 17 page