293 research outputs found
Revisiting random tensor models at large N via the Schwinger-Dyson equations
The Schwinger-Dyson Equations (SDEs) of matrix models are known to form
(half) a Virasoro algebra and have become a standard tool to solve matrix
models. The algebra generated by SDEs in tensor models (for random tensors in a
suitable ensemble) is a specific generalization of the Virasoro algebra and it
is important to show that these new symmetries determine the physical
solutions. We prove this result for random tensors at large N. Compared to
matrix models, tensor models have more than a single invariant at each order in
the tensor entries and the SDEs make them proliferate. However, the specific
combinatorics of the dominant observables allows to restrict to linear SDEs and
we show that they determine a unique physical perturbative solution. This gives
a new proof that tensor models are Gaussian at large N, with the covariance
being the full 2-point function.Comment: 17 pages, many figure
Coupling of hard dimers to dynamical lattices via random tensors
We study hard dimers on dynamical lattices in arbitrary dimensions using a
random tensor model. The set of lattices corresponds to triangulations of the
d-sphere and is selected by the large N limit. For small enough dimer
activities, the critical behavior of the continuum limit is the one of pure
random lattices. We find a negative critical activity where the universality
class is changed as dimers become critical, in a very similar way hard dimers
exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents
are calculated exactly. An alternative description as a system of
`color-sensitive hard-core dimers' on random branched polymers is provided.Comment: 12 page
The 1/N expansion of colored tensor models
In this paper we perform the 1/N expansion of the colored three dimensional
Boulatov tensor model. As in matrix models, we obtain a systematic topological
expansion, with more and more complicated topologies suppressed by higher and
higher powers of N. We compute the first orders of the expansion and prove that
only graphs corresponding to three spheres S^3 contribute to the leading order
in the large N limit.Comment: typos corrected, references update
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
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
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
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
Topological Graph Polynomials in Colored Group Field Theory
In this paper we analyze the open Feynman graphs of the Colored Group Field
Theory introduced in [arXiv:0907.2582]. We define the boundary graph
\cG_{\partial} of an open graph \cG and prove it is a cellular complex.
Using this structure we generalize the topological (Bollobas-Riordan) Tutte
polynomials associated to (ribbon) graphs to topological polynomials adapted to
Colored Group Field Theory graphs in arbitrary dimension
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
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
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