482 research outputs found
Asymptotic expansion of the multi-orientable random tensor model
Three-dimensional random tensor models are a natural generalization of the
celebrated matrix models. The associated tensor graphs, or 3D maps, can be
classified with respect to a particular integer or half-integer, the degree of
the respective graph. In this paper we analyze the general term of the
asymptotic expansion in N, the size of the tensor, of a particular random
tensor model, the multi-orientable tensor model. We perform their enumeration
and we establish which are the dominant configurations of a given degree.Comment: 27 pages, 24 figures, several minor modifications have been made, one
figure has been added; accepted for publication in "Electronic Journal of
Combinatorics
The Multi-Orientable Random Tensor Model, a Review
After its introduction (initially within a group field theory framework) in
[Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages,
arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last
years into a solid alternative of the celebrated colored (and colored-like)
random tensor model. In this paper we review the most important results of the
study of this MO model: the implementation of the expansion and of the
large limit ( being the size of the tensor), the combinatorial analysis
of the various terms of this expansion and finally, the recent implementation
of a double scaling limit
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
The Tensor Track, III
We provide an informal up-to-date review of the tensor track approach to
quantum gravity. In a long introduction we describe in simple terms the
motivations for this approach. Then the many recent advances are summarized,
with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion,
Osterwalder-Schrader positivity...) which, while important for the tensor track
program, are not detailed in the usual quantum gravity literature. We list open
questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure
Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
We study a just renormalizable tensorial group field theory of rank six with
quartic melonic interactions and Abelian group U(1). We introduce the formalism
of the intermediate field, which allows a precise characterization of the
leading order Feynman graphs. We define the renormalization of the model,
compute its (perturbative) renormalization group flow and write its expansion
in terms of effective couplings. We then establish closed equations for the two
point and four point functions at leading (melonic) order. Using the effective
expansion and its uniform exponential bounds we prove that these equations
admit a unique solution at small renormalized coupling.Comment: 37 pages, 14 figure
Random Tensors and Quantum Gravity
We provide an informal introduction to tensor field theories and to their
associated renormalization group. We focus more on the general motivations
coming from quantum gravity than on the technical details. In particular we
discuss how asymptotic freedom of such tensor field theories gives a concrete
example of a natural "quantum relativity" postulate: physics in the deep
ultraviolet regime becomes asymptotically more and more independent of any
particular choice of Hilbert basis in the space of states of the universe.Comment: Section 6 is essentially reproduced from author's arXiv:1507.04190
for self-contained purpose of the revie
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