Progress in the solving nonperturbative renormalization group for tensorial group field theory

Abstract

This manuscript aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian $U(1{)}^d$ models without closure constraint, especially we discuss the case of quartic melonic interaction. We present a new approach to solve the exact Wetterich flow equation called the effective vertex expansion method, and investigate the resulting flow equations, especially about the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward-Takahashi identities, and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a phase transition into the reduced phase space given by the Ward constraint.

arXiv comment37 pages. based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]

References in corpus (48)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Loop Quantum Gravity
• Optimisation of the exact renormalisation group
• An Introduction to the Nonperturbative Renormalization Group
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Colored Group Field Theory
• The 1/N expansion of colored tensor models
• Lectures on renormalization and asymptotic safety
• Derivative expansion and renormalisation group flows
• Quantum Cosmology from Group Field Theory Condensates: a Review
• 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
• Tensorial methods and renormalization in Group Field Theories
• The Tensor Track, III
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Effective average action in statistical physics and quantum field theory
• Some classes of renormalizable tensor models
• Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function
• Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
• Group field theories for all loop quantum gravity
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Cosmological perturbations from full quantum gravity
• 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
• Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Beta functions of $U(1{)}^d$ gauge invariant just renormalizable tensor models
• Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• 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
• A quantum field theory of simplicial geometry and the emergence of spacetime
• The Tensor Theory Space
• Constructive Tensor Field Theory
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Ward identity violation for melonic $T^4$-truncation
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Intersecting Connes Noncommutative Geometry with Quantum Gravity
• Ward-Takahashi identities for the colored Boulatov model
• Conserved Quantities in Background Independent Theories
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• Geometrogenesis under Quantum Graphity: problems with the ripening Universe

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• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Ward-constrained melonic renormalization group flow
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Reliability of the local truncations for the random tensor models renormalization group flow
• Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
• Flowing in discrete gravity models and Ward identities: A review
• Towards anisotropic cosmology in group field theory
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories