相关论文: Tensor models with generalized melonic interaction…

Generalized neutrino interactions (GNI) are emerging as a convenient framework for describing effective scalar, vector, and tensor interactions. Such interactions arise naturally from extensions of the Standard Model that aim to explain…

Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possess a novel large $N$ limit, where $g^2 N^3$ is held fixed. In this limit the perturbative expansion in the quartic coupling constant,…

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the…

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a $1/N$ expansion, and that at leading order they are dominated by melon diagrams. This proves the recent…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

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…

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian $p$-forms. In this work we introduce an index-free formulation of these…

Generalizations of vector field theories to tensors allow to similarly apply large-$N$ techniques but find a richer though often still tractable structure. However, the potential of such tensor theories has not been fully exploited since…

We present a many chain generalization of a recent work of ours, wherein an arbitrary number of fermionic chains are coupled via a Gauge interaction. Central to this construction is the role of an antisymmetric tensor which enters the…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

We apply the functional renormalization group to an Abelian Group Field Theory extended beyond the branched-polymer (melonic) sector by including interactions that are subdominant from a power-counting perspective but enhanced by derivative…

In this note, we study a melonic tensor model in $d$ dimensions based on three-index Dirac fermions with a four-fermion interaction. Summing the melonic diagrams at strong coupling allows one to define a formal large-$N$ saddle point in…

We study bosonic tensor field theories with sextic interactions in $d<3$ dimensions. We consider two models, with rank-3 and rank-5 tensors, and $U(N)^3$ and $O(N)^5$ symmetry, respectively. For both of them we consider two variations: one…

In this paper we identify and analyze in detail the subleading contributions in the 1/N expansion of random tensors, in the simple case of a quartically interacting model. The leading order for this 1/N expansion is made of graphs, called…

We study a set of large-$N$ tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised…

The rank three tensor model with tetrahedral interaction was shown by Carrozza and Tanasa to admit a $1/N$ expansion, dominated by melonic diagrams, and double tadpoles decorated with melons at next-to-leading order. This model has…

We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank five and higher. They are the non-random counterparts of the Sachdev-Ye-Kitaev (SYK) models where the Hamiltonian couples six or…

The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large $N$ limit known as the melonic limit that is strongly coupled yet…

We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue of a typical tensor in this ensemble by examining the rate of…

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…