Group Field Theory: An overview

Abstract

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.

10 pages

Cited by in corpus (223)

• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Critical behavior of colored tensor models in the large N limit
• The principle of relative locality
• A New Spin Foam Model for 4d Gravity
• Colored Tensor Models - a Review
• The loop-quantum-gravity vertex-amplitude
• SU(N) gauge theories at large N
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Colored Group Field Theory
• Flipped spinfoam vertex and loop gravity
• Graviton propagator from background-independent quantum gravity
• The 1/N expansion of colored tensor models in arbitrary dimension
• The 1/N expansion of colored tensor models
• Homogeneous cosmologies as group field theory condensates
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Loop Quantum Gravity: An Inside View
• Phase space descriptions for simplicial 4d geometries
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Group field theory renormalization - the 3d case: power counting of divergences
• Double Scaling in Tensor Models with a Quartic Interaction
• Topological Graph Polynomials in Colored Group Field Theory
• LQG propagator from the new spin foams
• Bosonic Colored Group Field Theory
• $O(N)$ Random Tensor Models
• A generalization of the Virasoro algebra to arbitrary dimensions
• Scaling behaviour of three-dimensional group field theory
• Linearized Group Field Theory and Power Counting Theorems
• Diffeomorphisms in group field theories
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The Tensor Track, III
• Tensor models and embedded Riemann surfaces
• Einstein-Cartan wormhole solutions
• Ten questions on Group Field Theory (and their tentative answers)
• Non-Gaussianity as a signature of a quantum theory of gravity
• EPRL/FK Group Field Theory
• Loop quantum gravity: the first twenty five years
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Bubble divergences from cellular cohomology
• Lost in Translation: Topological Singularities in Group Field Theory
• Flowing in Group Field Theory Space: a Review
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Spin Foams and Canonical Quantization
• Emergent Models for Gravity: an Overview of Microscopic Models
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Lorentzian LQG vertex amplitude
• Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function
• Multi-orientable Group Field Theory
• Self-energy and vertex radiative corrections in LQG
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
• The Multi-Orientable Random Tensor Model, a Review
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Ward identities and combinatorics of rainbow tensor models
• 4d Deformed Special Relativity from Group Field Theories
• Path integral representation of spin foam models of 4d gravity
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
• Path integral measure and triangulation independence in discrete gravity
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Renormalization Group Flow of the Holst Action
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Generalised uncertainty relations from superpositions of geometries
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Coarse graining flow of spin foam intertwiners
• Quantum gravity and gravitational-wave astronomy
• Spin foam model from canonical quantization
• Emergence of a low spin phase in group field theory condensates
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Dimensional flow in discrete quantum geometries
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Group field theory condensate cosmology: An appetizer
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• A relational Hamiltonian for group field theory
• Algebraic structures in quantum gravity
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Critical Overview of Loops and Foams
• Group field theory formulation of 3d quantum gravity coupled to matter fields
• Random Tensors and Quantum Gravity
• Bubble divergences: sorting out topology from cell structure
• Bubble divergences from twisted cohomology
• Spacetime foam: a review
• A Deformed Poincare Invariance for Group Field Theories
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Uniqueness of canonical tensor model with local time
• LQG propagator: III. The new vertex
• A quantum field theory of simplicial geometry and the emergence of spacetime
• Linking covariant and canonical LQG II: Spin foam projector
• Effective Hamiltonian Constraint from Group Field Theory
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Super tensor models, super fuzzy spaces and super n-ary transformations
• Relational evolution of effectively interacting GFT quantum gravity condensates
• Constructive tensor field theory: The $T_4^4$ model
• Group Field Theory in dimension four minus epsilon
• Fermions in three-dimensional spinfoam quantum gravity
• Coupling gauge theory to spinfoam 3d quantum gravity
• Interpreting canonical tensor model in minisuperspace
• Background independent condensed matter models for quantum gravity
• Causality and matter propagation in 3d spin foam quantum gravity
• Generalised effective cosmology from group field theory
• Quantum canonical tensor model and an exact wave function
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Emergence of Spacetime in a restricted Spin-foam model
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Phantom-like dark energy from quantum gravity
• Comment on `Lost in Translation: Topological Singularities in Group Field Theory'
• Spinors and Voros star-product for Group Field Theory: First Contact
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Mean-field phase transitions in TGFT quantum gravity
• Generalised group field theories and quantum gravity transition amplitudes
• Perturbing a quantum gravity condensate
• Phase transitions in group field theory: The Landau perspective
• Matrix Models as Non-commutative Field Theories on R^3
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Thermal quantum gravity condensates in group field theory cosmology
• The full Ward-Takahashi Identity for colored tensor models
• Inequivalent coherent state representations in group field theory
• A simple proof of orientability in colored group field theory
• (No) phase transition in tensorial group field theory
• Hamiltonian group field theory with multiple scalar matter fields
• Feynman diagrammatic approach to spin foams
• Group field theory and simplicial quantum gravity
• Bulk amplitude and degree of divergence in 4d spin foams
• Thermal representations in group field theory: squeezed vacua and quantum gravity condensates
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Discrete and continuum third quantization of Gravity
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Emergent gravitational dynamics from multi-BEC hydrodynamics?
• Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Quantum Gravity on the computer: Impressions of a workshop
• q-Deformed spin foam models of quantum gravity
• Emergent Braided Matter of Quantum Geometry
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Encoding simplicial quantum geometry in group field theories
• Quantum Gravity with Matter via Group Field Theory
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• Corner symmetry and quantum geometry
• Loop Quantum Gravity's Boundary Maps
• Thermal quantum spacetime
• A canonical rank-three tensor model with a scaling constraint
• Emergent matter from 3d generalised group field theories
• Addendum to "Relational Hamiltonian for group field theory"
• Random volumes from matrices
• Holographic entanglement in spin network states: a focused review
• Consequences of Godel Theorems on Third Quantized Theories Like String Field Theory and Group Field Theory
• Towards anisotropic cosmology in group field theory
• Time-space duality in 2D quantum gravity
• Ward-Takahashi identities for the colored Boulatov model
• Towards a Loop Quantum Gravity and Yang-Mills Unification
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Piecewise linear loop quantum gravity
• Surgery in colored tensor models
• A finiteness bound for the EPRL/FK spin foam model
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Tensorial Structure of the LQG graviton propagator
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• A Renormalizable SYK-type Tensor Field Theory
• Minimizers of the dynamical Boulatov model
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• Classical Group Field Theory
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Spheres are rare
• Quantum Gravity and Cosmology: an intimate interplay
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
• Second-order amplitudes in loop quantum gravity
• Matter fields in triangle-hinge models
• Intertwiner Entanglement Excitation and Holonomy Operator
• Translation-Invariant Noncommutative Renormalization
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Curvature effects in the spectral dimension of spin foams
• Stochastic dynamics for Group Field Theories
• Super-group field cosmology in Batalin-Vilkovisky formulation
• Geometrogenesis in GFT: An Analysis
• Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"
• Quantum gravity and gravitational-wave astronomy
• Relational dynamics and Page-Wootters formalism in group field theory
• Radiative corrections to the EPRL-FK spinfoam graviton
• An $OSp$ extension of Canonical Tensor Model
• Genus dependence of the number of (non-)orientable surface triangulations
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• Stationary cosmology in group field theory
• A Diagrammatic Equation for Oriented Planar Graphs
• Quantum black holes as classical space factories
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Hilbert space formalisms for group field theory
• Reconstructing the metric in group field theory
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Open-closed 3d gravity as a random ensemble
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
• Emergence of scalar matter from spinfoam model
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Weighting bubbles in group field theory
• Foundational Issues in Group Field Theory
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications
• World quantum gravity: Quantum test objects and Synge's world function
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model
• Boundary State Stability under Spinfoam Evolution for the Quantum 4-Simplex
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• Combinatorial Spacetime from Loop Quantum Gravity
• Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, $3j$ Symbols, and Character Localization
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• Cosmological implications of the hydrodynamical phase of group field theory
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime
• Are there any Landau poles in wavelet-based quantum field theory?
• Hessian in the spinfoam models with cosmological constant