119 research outputs found
Constructive Matrix Theory
We extend the technique of constructive expansions to compute the connected
functions of matrix models in a uniform way as the size of the matrix
increases. This provides the main missing ingredient for a non-perturbative
construction of the field theory on the Moyal four
dimensional space.Comment: 12 pages, 3 figure
Partial duality of hypermaps
We introduce a collection of new operations on hypermaps, partial duality,
which include the classical Euler-Poincar\'e dualities as particular cases.
These operations generalize the partial duality for maps, or ribbon graphs,
recently discovered in a connection with knot theory. Partial duality is
different from previous studied operations of S. Wilson, G. Jones, L. James,
and A. Vince. Combinatorially hypermaps may be described in one of three ways:
as three involutions on the set of flags (-model), or as three
permutations on the set of half-edges (-model in orientable case), or
as edge 3-colored graphs. We express partial duality in each of these models.Comment: 19 pages, 16 figure
Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
We prove that the beta function of the Grosse-Wulkenhaar model including a
magnetic field vanishes at all order of perturbations. We compute the
renormalization group flow of the relevant dynamic parameters and find a
non-Gaussian infrared fixed point. Some consequences of these results are
discussed.Comment: 14 pages, 5 figure
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
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
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
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
Vanishing of Beta Function of Non Commutative Theory to all orders
The simplest non commutative renormalizable field theory, the model
on four dimensional Moyal space with harmonic potential is asymptotically safe
up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.
Rivasseau. We extend this result to all orders.Comment: 12 pages, 3 figure
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
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