The Tensor Track, III

Abstract

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.

53 pages, 6 figures

References in corpus (42)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Quantum Graphity: a model of emergent locality
• Group field theory with non-commutative metric variables
• The 1/N expansion of colored tensor models
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• The causal set approach to quantum gravity
• Group field theory renormalization - the 3d case: power counting of divergences
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Scaling behaviour of three-dimensional group field theory
• A translation-invariant renormalizable non-commutative scalar model
• Tensorial methods and renormalization in Group Field Theories
• EPRL/FK Group Field Theory
• Moments and Cumulants of Polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
• Lost in Translation: Topological Singularities in Group Field Theory
• Constructive ${\varphi }^4$ field theory without tears
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• The spectral dimension of generic trees
• Conformal Random Geometry
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Parametric Representation of Noncommutative Field Theory
• Group field theory as the 2nd quantization of Loop Quantum Gravity
• Duality and KPZ in Liouville Quantum Gravity
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Progress in solving a noncommutative quantum field theory in four dimensions
• A quantum field theory of simplicial geometry and the emergence of spacetime
• Generalized constructive tree weights
• Group Field Theory in dimension four minus epsilon
• Constructive Tensor Field Theory: The $T_3^4$ Model
• An analysis of the intermediate field theory of $T^4$ tensor model
• Universality in p-spin glasses with correlated disorder
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Disappearance and emergence of space and time in quantum gravity
• Vanishing dimensions: theory and phenomenology
• Counting Line-Colored D-ary Trees
• A Givental-like Formula and Bilinear Identities for Tensor Models
• Trees of nuclei and bounds on the number of triangulations of the 3-ball
• Cataloguing PL 4-manifolds by gem-complexity

Cited by in corpus (66)

• The nonperturbative functional renormalization group and its applications
• Quantum Cosmology from Group Field Theory Condensates: a Review
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Invitation to Random Tensors
• The Multi-Orientable Random Tensor Model, a Review
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Functional Renormalization Group Approach for Tensorial Group Field Theory: A Rank-6 Model with Closure Constraint
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Closed equations of the two-point functions for tensorial group field theory
• The double scaling limit of the multi-orientable tensor model
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Random Tensors and Quantum Gravity
• Why are tensor field theories asymptotically free?
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• The Tensor Theory Space
• Nonperturbative renormalization for the neural network-QFT correspondence
• Constructive Tensor Field Theory
• Group Field Theory in dimension four minus epsilon
• The Fock Space of Loopy Spin Networks for Quantum Gravity
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Constructive tensor field theory: The $T_4^4$ model
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Gauge theories on quantum spaces
• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• Ward identity violation for melonic $T^4$-truncation
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Symmetry breaking in tensor models
• Conformality of $1/N$ corrections in SYK-like models
• Towards background independent quantum gravity with tensor models
• Asymptotic expansion of the multi-orientable random tensor model
• Loop Vertex Expansion for Higher Order Interactions
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• The full Ward-Takahashi Identity for colored tensor models
• Inequivalent coherent state representations in group field theory
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Phase Transition in Tensor Models
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting
• Flowing in discrete gravity models and Ward identities: A review
• Renormalizable Tensor Field Theories
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
• Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
• Renormalization procedure for random tensor networks and the canonical tensor model
• All-orders asymptotics of tensor model observables from symmetries of restricted partitions
• Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• Non-commutative quantum geometric data in group field theories
• Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"
• A power counting theorem for a $p^{2a}{\varphi }^4$ tensorial group field theory
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• A Givental-like Formula and Bilinear Identities for Tensor Models
• The Multiscale Loop Vertex Expansion
• Random Tensor models: Combinatorics, Geometry, Quantum Gravity and Integrability
• Aspects of quantum gravity
• Is the local linearity of space-time inherited from the linearity of probabilities?
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers
• Can we make sense out of "Tensor Field Theory"?