Related papers: Quantum Gravity and Random Tensors
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
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…
In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…
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…
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…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
The main purpose of this paper is to introduce the random tensor with normal distribution, which promotes the matrix normal distribution to a higher order case. Some basic knowledge on tensors are introduced before we focus on the random…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
This note is a sequel to the previous series "Tensor Track I-III". Assuming some familiarity with the tensor track approach to quantum gravity, we provide a brief introduction to the developments of the last two years and to their…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…
Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in…
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,…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…