Critical behavior of colored tensor models in the large N limit

Abstract

Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.

20 pages

References in corpus (3)

• Group field theory renormalization - the 3d case: power counting of divergences
• Scaling behaviour of three-dimensional group field theory
• Lost in Translation: Topological Singularities in Group Field Theory

Cited by in corpus (229)

• The Spin Foam Approach to Quantum Gravity
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The Bulk Dual of SYK: Cubic Couplings
• The complete $1/N$ expansion of a SYK--like tensor model
• An introduction to the SYK model
• Melons are branched polymers
• All point correlation functions in SYK
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Double Scaling in Tensor Models with a Quartic Interaction
• Quantum Chaos and Holographic Tensor Models
• $O(N)$ Random Tensor Models
• Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
• A Supersymmetric SYK-like Tensor Model
• A generalization of the Virasoro algebra to arbitrary dimensions
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Tensorial methods and renormalization in Group Field Theories
• Coarse graining methods for spin net and spin foam models
• The Tensor Track, III
• Ten questions on Group Field Theory (and their tentative answers)
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Notes on Melonic $O(N{)}^{q-1}$ Tensor Models
• Revisiting random tensor models at large N via the Schwinger-Dyson equations
• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• Spectra of Operators in Large $N$ Tensor Models
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Flowing in Group Field Theory Space: a Review
• Some classes of renormalizable tensor models
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Phase Transition in Dually Weighted Colored Tensor Models
• The Ising Model on Random Lattices in Arbitrary Dimensions
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Invitation to Random Tensors
• New 1/N expansions in random tensor models
• Random Matrices and Holographic Tensor Models
• The 1/N expansion of multi-orientable random tensor models
• Correlators in tensor models from character calculus
• Renormalization Group Flow in CDT
• Ward identities and combinatorics of rainbow tensor models
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• Functional Renormalization Group Approach for Tensorial Group Field Theory: A Rank-6 Model with Closure Constraint
• The Large D Limit of Einstein's Equations
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Quenched equals annealed at leading order in the colored SYK model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Prismatic Large $N$ Models for Bosonic Tensors
• Melonic phase transition in group field theory
• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• 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
• Symmetry Breaking in Coupled SYK or Tensor Models
• The spectral dimension of simplicial complexes: a renormalization group theory
• SYK-like Tensor Models on the Lattice
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three
• The double scaling limit of the multi-orientable tensor model
• Vector models and generalized SYK models
• Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Multicritical tensor models and hard dimers on spherical random lattices
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Quantum group spin nets: refinement limit and relation to spin foams
• Contrasting SYK-like Models
• Phases Of Melonic Quantum Mechanics
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Tensorial Gross-Neveu models
• Addendum to "A Renormalizable 4-Dimensional Tensor Field Theory"
• The $1/N$ expansion of tensor models with two symmetric tensors
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Canonical tensor models with local time
• Cut and join operator ring in Aristotelian tensor model
• Black Holes as Quantum Gravity Condensates
• Random Tensors and Quantum Gravity
• Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
• Why are tensor field theories asymptotically free?
• Bubbles and jackets: new scaling bounds in topological group field theories
• Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Towards a Finite-$N$ Hologram
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Uniqueness of canonical tensor model with local time
• The Tensor Theory Space
• Super tensor models, super fuzzy spaces and super n-ary transformations
• Large $N$ Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension $d\ge 2$
• Line of fixed points in a bosonic tensor model
• Notes on Matrix Models
• Multi-critical behaviour of 4-dimensional tensor models up to order 6
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• An analysis of the intermediate field theory of $T^4$ tensor model
• More on the New Large $D$ Limit of Matrix Models
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Topology in colored tensor models via crystallization theory
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Combinatorial aspects of the Sachdev-Ye-Kitaev model
• Coupling of hard dimers to dynamical lattices via random tensors
• A Renormalizable 4-Dimensional Tensor Field Theory
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Ward identity violation for melonic $T^4$-truncation
• Spectrum of Majorana Quantum Mechanics with $O(4{)}^3$ Symmetry
• The higher-order spectrum of simplicial complexes: a renormalization group approach
• Towards the map of quantum gravity
• From Kronecker to tableau pseudo-characters in tensor models
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Emergence of Spacetime in a restricted Spin-foam model
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• Universality in p-spin glasses with correlated disorder
• Symmetry breaking in tensor models
• On Melonic Supertensor Models
• Conformality of $1/N$ corrections in SYK-like models
• A 3d disordered superconformal fixed point
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Towards background independent quantum gravity with tensor models
• Loop Vertex Expansion for Higher Order Interactions
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Higher melonic theories
• (No) phase transition in tensorial group field theory
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• Bulk amplitude and degree of divergence in 4d spin foams
• Coherent states for quantum gravity: towards collective variables
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Phase Transition in Tensor Models
• Renormalizable Models in Rank $d\ge 2$ Tensorial Group Field Theory
• Canonical tensor model through data analysis -- Dimensions, topologies, and geometries --
• The tri-fundamental quartic model
• Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
• Holographic maps from quantum gravity states as tensor networks
• The F-theorem in the melonic limit
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory
• Melonic dominance and the largest eigenvalue of a large random tensor
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• Reliability of the local truncations for the random tensor models renormalization group flow
• Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
• Emergent symmetries in the canonical tensor model
• Gravity as an emergent phenomenon: a GFT perspective
• Towards computational insights into the large-scale structure of spin foams
• Flowing in discrete gravity models and Ward identities: A review
• On the large $D$ expansion of Hermitian multi-matrix models
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• A random matrix model with non-pairwise contracted indices
• Remarks on a melonic field theory with cubic interaction
• Hagedorn Temperature in Large $N$ Majorana Quantum Mechanics
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Renormalizable Tensor Field Theories
• Maximizing the number of edges in three-dimensional colored triangulations whose building blocks are balls
• Ward-Takahashi identities for the colored Boulatov model
• On the generalization of the Wigner semicircle law to real symmetric tensors
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Melonic Turbulence
• Diagrammatic proof of the large $N$ melonic dominance in the SYK model
• Surgery in colored tensor models
• Complete Solution of a Gauged Tensor Model
• Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• Generalized cut operation associated with higher order variation in tensor models
• A Renormalizable SYK-type Tensor Field Theory
• All-orders asymptotics of tensor model observables from symmetries of restricted partitions
• The new spin foam models and quantum gravity
• Holography for Tensor models
• Double scaling limit of multi-matrix models at large $D$
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• Classical Group Field Theory
• Supersymmetric Landau-Ginzburg Tensor Models
• Spheres are rare
• Stochastic dynamics for Group Field Theories
• The Ergodicity Landscape of Quantum Theories
• Emergent classical geometries on boundaries of randomly connected tensor networks
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Sextic tensor model in rank $3$ at next-to-leading order
• $(D+1)$-Colored Graphs - a Review of Sundry Properties
• On the number of coloured triangulations of $d$-manifolds
• Counting Line-Colored D-ary Trees
• Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations
• Note on the Intermediate Field Representation of Phi^2k Theory in Zero Dimension
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• A power counting theorem for a $p^{2a}{\varphi }^4$ tensorial group field theory
• An $OSp$ extension of Canonical Tensor Model
• GEMs and amplitude bounds in the colored Boulatov model
• Classifying compact 4-manifolds via generalized regular genus and G-degree
• A Givental-like Formula and Bilinear Identities for Tensor Models
• Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model
• Radiative corrections to the EPRL-FK spinfoam graviton
• Aspects of quantum gravity
• Splitting-merging transitions in tensor-vectors systems in exact large-$N$ limits
• Sextic tensor field theories in rank $3$ and $5$
• Backgrounds from Tensor Models: A Proposal
• Tensor Field Theories: Renormalization and Random Geometry
• Phase profile of the wave function of canonical tensor model and emergence of large spacetimes
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models
• The Tensor Track VII: From Quantum Gravity to Artificial Intelligence
• Stochastic melonic kinetics with random initial conditions
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Another proof of the $1/N$ expansion of the rank three tensor model with tetrahedral interaction
• Tensor models from the viewpoint of matrix models: the case of the Gaussian distribution
• Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
• Mother canonical tensor model
• The Non-melonic Sector of Tensor Models and Gravity
• Melonic large $N$ limit of $5$-index irreducible random tensors
• The Tensor Track VIII: Stochastic Analysis
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• Asymptotic probability for connectedness
• Emergence of Lie group symmetric classical spacetimes in canonical tensor model
• Singular topologies in the Boulatov model
• Quartic Tensor Models
• Tensor Models: extending the matrix models structures and methods
• Landau Theory of Causal Dynamical Triangulations
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers
• Phases of Tree-decorated Dynamical Triangulations in 3D
• A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product
• Can we make sense out of "Tensor Field Theory"?