Invitation to Random Tensors

Abstract

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. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.

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• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
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• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• Identifying cosmological perturbations in group field theory condensates
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• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
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Cited by in corpus (51)

• The nonperturbative functional renormalization group and its applications
• A Supersymmetric SYK-like Tensor Model
• The universe as a quantum gravity condensate
• How perturbative is quantum gravity?
• Random Matrices and Holographic Tensor Models
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Multi-critical behaviour of 4-dimensional tensor models up to order 6
• Liouville theory and Matrix models: A Wheeler DeWitt perspective
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Mean-field phase transitions in TGFT quantum gravity
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Abelian Tensor Models on the Lattice
• (No) phase transition in tensorial group field theory
• Inequivalent coherent state representations in group field theory
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
• Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
• Reliability of the local truncations for the random tensor models renormalization group flow
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Quantum Gravity on the computer: Impressions of a workshop
• Emergent Space-Time via a Geometric Renormalization Method
• An asymptotically safe guide to quantum gravity and matter
• From Noncommutative Geometry to Random Matrix Theory
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• Complete Solution of a Gauged Tensor Model
• Minimizers of the dynamical Boulatov model
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Stochastic dynamics for Group Field Theories
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• On the number of coloured triangulations of $d$-manifolds
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• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
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• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Functional Renormalization Group Approach for Signal Detection
• Can we make sense out of "Tensor Field Theory"?