Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory

Abstract

This paper aims at giving a novel approach to investigate the behavior of the renormalization group flow for tensorial group field theories to all orders of the perturbation theory. From an appropriate choice of the kinetic kernel, we build an infinite family of just-renormalizable models, for tensor fields with arbitrary rank $d$. Investigating the large $d$ limit, we show that the self-energy melonic amplitude is decomposed as a product of loop-vertex functions, depending only on dimensionless mass. The corresponding melonic amplitudes may be mapped as trees in the so-called Hubbard-Stratonivich representation, and we show that only trees with edges of different colors survive in the large $d$-limit. These two key features allow us to resum the perturbative expansion for self-energy, providing an explicit expression for arbitrary external momenta in terms of Lambert function. Finally, inserting this resumed solution into the Callan-Symanzik equations, and taking into account the strong relation between two and four-point functions arising from melonic Ward-Takahashi identities, we then deduce an explicit expression for relevant and marginal $\beta$-functions, valid to all orders of the perturbative expansion. By investigating the solutions of the resulting flow, we conclude about the non-existence of any fixed point in the investigated region of the full phase space.

arXiv comment50 pages 5 figures

References in corpus (63)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• 2D Gravity and Random Matrices
• Loop Quantum Gravity
• Critical behavior of colored tensor models in the large N limit
• A Model of Three-Dimensional Lattice Gravity
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• The 1/N expansion of colored tensor models in arbitrary dimension
• Renormalization Group Approach to Matrix Models
• Melons are branched polymers
• Group field theory renormalization - the 3d case: power counting of divergences
• Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The universe as a quantum gravity condensate
• Spin foam model for Lorentzian General Relativity
• Tensorial methods and renormalization in Group Field Theories
• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• How to Resum Feynman Graphs
• Phase Transition in Dually Weighted Colored Tensor Models
• Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function
• Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
• 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
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Cosmological perturbations from full quantum gravity
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• 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
• Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
• 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
• Black Holes as Quantum Gravity Condensates
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Group field theory and its cosmology in a matter reference frame
• Constructive Tensor 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
• Inhomogeneous universe from group field theory condensate
• Ward identity violation for melonic $T^4$-truncation
• Generalised group field theories and quantum gravity transition amplitudes
• Towards background independent quantum gravity with tensor models
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Group field theory and simplicial quantum gravity
• Solution of all quartic matrix models
• Lambert-W solves the noncommutative ${\Phi }^4$-model
• Solution of the self-dual ${\Phi }^4$ QFT-model on four-dimensional Moyal space
• Exact solution of matricial ${\Phi }_2^3$ quantum field theory
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Conserved Quantities in Background Independent Theories
• Schwinger-Dyson equation in three-dimensional simplicial quantum gravity
• Ultralocal nature of geometrogenesis
• Counting Line-Colored D-ary Trees
• A Solvable Tensor Field Theory
• Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations
• On enumeration of tree-rooted planar cubic maps. II
• On enumeration of tree-rooted planar cubic maps

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