Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions

Abstract

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.

51 pages, 15 figures, 2 tables. v2: minor corrections. v3: matches published version

References in corpus (11)

• LQG vertex with finite Immirzi parameter
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Flipped spinfoam vertex and loop gravity
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• The 1/N expansion of colored tensor models
• Group field theory renormalization - the 3d case: power counting of divergences
• EPRL/FK Group Field Theory
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Constructive ${\varphi }^4$ field theory without tears
• Bubbles and jackets: new scaling bounds in topological group field theories
• Universality in p-spin glasses with correlated disorder

Cited by in corpus (79)

• Homogeneous cosmologies as group field theory condensates
• $O(N)$ Random Tensor Models
• Quantum Cosmology from Group Field Theory Condensates: a Review
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Flowing in Group Field Theory Space: a Review
• Invitation to Random Tensors
• Multifractional theories: an unconventional review
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• Horizon entropy from quantum gravity condensates
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Closed equations of the two-point functions for tensorial group field theory
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Boosting Wigner's nj-symbols
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Tensorial Gross-Neveu models
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• Quantum cosmology of (loop) quantum gravity condensates: An example
• Random Tensors and Quantum Gravity
• Why are tensor field theories asymptotically free?
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Group field theory and its cosmology in a matter reference frame
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Large $N$ Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension $d\ge 2$
• Constructive Tensor Field Theory
• Loop quantum cosmology from group field theory
• Constructive tensor field theory: The $T_4^4$ model
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Group Field Theory in dimension four minus epsilon
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Inhomogeneous universe from group field theory condensate
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Exact Renormalisation Group Equations and Loop Equations for Tensor Models
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Identifying cosmological perturbations in group field theory condensates
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Symmetry breaking in tensor models
• Perturbing a quantum gravity condensate
• Fisher Metric, Geometric Entanglement and Spin Networks
• Loop Vertex Expansion for Higher Order Interactions
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• Infrared divergences in the EPRL-FK Spin Foam model
• Hamiltonian group field theory with multiple scalar matter fields
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Ward-constrained melonic renormalization group flow
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Phase Transition in Tensor Models
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Reliability of the local truncations for the random tensor models renormalization group flow
• Flowing in discrete gravity models and Ward identities: A review
• Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Melonic Turbulence
• Surgery in colored tensor models
• Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
• A Renormalizable SYK-type Tensor Field Theory
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Stochastic dynamics for Group Field Theories
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• The tensor Harish-Chandra-Itzykson-Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• Weighting bubbles in group field theory
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• An intriguing connection between Pisarski's fixed point and (2+3)-spin glasses
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• Effective cosmology from one-body operators in group field theory