Scale invariance beyond criticality within the mean-field analysis of tensorial field theories

Abstract

We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.

arXiv comment45 pages, 2 figures, 1 table; closest to published version

References in corpus (84)

• Gauge Theory Correlators from Non-Critical String Theory
• Modified Gravity and Cosmology
• f(R) theories
• Background Independent Quantum Gravity: A Status Report
• Wilson loops in large N field theories
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The Spin Foam Approach to Quantum Gravity
• The nonperturbative functional renormalization group and its applications
• Spin Foam Models for Quantum Gravity
• f(R) Gravity and scalar-tensor theory
• An Introduction to the Nonperturbative Renormalization Group
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Group Field Theory: An overview
• A Lorentzian Signature Model for Quantum General Relativity
• Colored Group Field Theory
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
• Group field theory with non-commutative metric variables
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• The complete $1/N$ expansion of a SYK--like tensor model
• An introduction to the SYK model
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• $O(N)$ Random Tensor Models
• Non-commutative Renormalization
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Spin foam model for Lorentzian General Relativity
• The universe as a quantum gravity condensate
• Tensorial methods and renormalization in Group Field Theories
• Spin foam models for quantum gravity from lattice path integrals
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Non-commutative flux representation for loop quantum gravity
• Lost in Translation: Topological Singularities in Group Field Theory
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• Quantum Gravity via Causal Dynamical Triangulations
• Functional Renormalization Group Approach for Tensorial Group Field Theory: A Rank-6 Model with Closure Constraint
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Critical behavior in spherical and hyperbolic spaces
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• 2PI effective action for the SYK model and tensor field theories
• Cosmological aspects of the Eisenhart-Duval lift
• Symmetry Breaking in Coupled SYK or Tensor Models
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• 3+1 spinfoam model of quantum gravity with spacelike and timelike components
• Tutorial on Scale and Conformal Symmetries in Diverse Dimensions
• Eisenhart lifts and symmetries of time-dependent systems
• Group field theory for quantum gravity minimally coupled to a scalar field
• Group field theory condensate cosmology: An appetizer
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Group field theory and its cosmology in a matter reference frame
• The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics
• Line of fixed points in a bosonic tensor model
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Mean-field phase transitions in TGFT quantum gravity
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Noncommutative QFT and Renormalization
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Phase transitions in group field theory: The Landau perspective
• Towards background independent quantum gravity with tensor models
• (No) phase transition in tensorial group field theory
• Functional Renormalization of Noncommutative Scalar Field Theory
• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Schrödinger Symmetry in Gravitational Mini-Superspaces
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Flowing in discrete gravity models and Ward identities: A review
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• Spinfoams: Foundations
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Stochastic dynamics for Group Field Theories
• Correlation Functions of a Conformal Field Theory in Three Dimensions

Cited by in corpus (2)

• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model