Related papers: The Multi-Orientable Random Tensor Model, a Review

In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model. From a combinatorial point of view, we find the class of Feynman tensor graphs…

Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum limit accessible analytically. In this…

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…

Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of…

Although random tensor models were introduced twenty years ago, it is only in 2011 that Gurau proved the existence of a 1/N expansion. Here we show that there actually is more than a single 1/N expansion, depending on the dimension. These…

Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…

We study a connection between random tensors and random matrices through $U(\tau)$ matrix models which generate fully packed, oriented loops on random surfaces. The latter are found to be in bijection with a set of regular edge-colored…

Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this…

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…

We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…

We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this…

The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion,…

Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…

In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using…

Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…

Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…

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.

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results…