419 research outputs found
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
Dimensional regularization and renormalization of non-commutative QFT
Using the recently introduced parametric representation of non-commutative
quantum field theory, we implement here the dimensional regularization and
renormalization of the vulcanized model on the Moyal space.Comment: 31 pages, 8 figure
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
Singular topologies in the Boulatov model
Through the question of singular topologies in the Boulatov model, we
illustrate and summarize some of the recent advances in Group Field Theory.Comment: 4 pages; proceedings of Loops'11 (May 2011, Madrid); v2: minor
modifications matching published versio
The double scaling limit of the multi-orientable tensor model
In this paper we study the double scaling limit of the multi-orientable
tensor model. We prove that, contrary to the case of matrix models but
similarly to the case of invariant tensor models, the double scaling series are
convergent. We resum the double scaling series of the two point function and of
the leading singular part of the four point function. We discuss the behavior
of the leading singular part of arbitrary correlation functions. We show that
the contribution of the four point function and of all the higher point
functions are enhanced in the double scaling limit. We finally show that all
the correlation functions exhibit a singularity at the same critical value of
the double scaling parameter which, combined with the convergence of the double
scaling series, suggest the existence of a triple scaling limit
Uniform random colored complexes
We present here random distributions on -edge-colored, bipartite
graphs with a fixed number of vertices . These graphs are dual to
-dimensional orientable colored complexes. We investigate the behavior of
quantities related to those random graphs, such as their number of connected
components or the number of vertices of their dual complexes, as . The techniques involved in the study of these quantities also yield a
Central Limit Theorem for the genus of a uniform map of order , as .Comment: 36 pages, 9 figures, minor additions and correction
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
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
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
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