Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space

Abstract

Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantum gravity model arises naturally from a theory of this type, but restricted to the homogeneous space S^3=SO(4)/SO(3), as a term in its Feynman expansion. From such a perspective, 4d quantum spacetime emerges as a Feynman graph, in the manner of the 2d matrix models. This formalism provides a precise meaning to the ``sum over triangulations'', which is presumably necessary for a physical interpretation of a spin foam model as a theory of gravity. In addition, this formalism leads us to introduce a natural alternative model, which might have relevance for quantum gravity.

16 Pages (RevTeX), 4 eps figures. Minor revisions in the definition of the model

Cited by in corpus (163)

• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• A Short Review of Loop Quantum Gravity
• Group Field Theory: An overview
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Flipped spinfoam vertex and loop gravity
• Graviton propagator from background-independent quantum gravity
• Spacetime as a Feynman diagram: the connection formulation
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Group field theory with non-commutative metric variables
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• Homogeneous cosmologies as group field theory condensates
• Diffeomorphisms and spin foam models
• Melons are branched polymers
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• 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
• An invitation to loop quantum gravity
• Quantum gravity with a positive cosmological constant
• Quantum Cosmology from Group Field Theory Condensates: a Review
• A spin foam model without bubble divergences
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Quantum gravity in terms of topological observables
• Spin foam model for Lorentzian General Relativity
• Tensorial methods and renormalization in Group Field Theories
• Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4
• Asymptotics of 6j and 10j symbols
• Loop quantum gravity: the first twenty five years
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Lost in Translation: Topological Singularities in Group Field Theory
• Flowing in Group Field Theory Space: a Review
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Non-perturbative summation over 3D discrete topologies
• Lorentzian LQG vertex amplitude
• Finiteness of a spinfoam model for euclidean quantum general relativity
• Multi-orientable Group Field Theory
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Self-energy and vertex radiative corrections in LQG
• Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Path integral representation of spin foam models of 4d gravity
• 4d Deformed Special Relativity from Group Field Theories
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Categorical representations of categorical groups
• Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity
• Implementing causality in the spin foam quantum geometry
• Integrability for Relativistic Spin Networks
• Spin Foam Models of Riemannian Quantum Gravity
• 3+1 spinfoam model of quantum gravity with spacelike and timelike components
• A spin foam model for pure gauge theory coupled to quantum gravity
• Minkowski vacuum in background independent quantum gravity
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• A finiteness proof for the Lorentzian state sum spinfoam model for quantum general relativity
• A relational Hamiltonian for group field theory
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Critical Overview of Loops and Foams
• Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
• The linearization of the Kodama state
• Canonical tensor models with local time
• Group field theory formulation of 3d quantum gravity coupled to matter fields
• Infinite-Dimensional Representations of 2-Groups
• Renormalization of Discrete Models without Background
• Spin Foam Diagrammatics and Topological Invariance
• Uniqueness of canonical tensor model with local time
• Group field theory and its cosmology in a matter reference frame
• A Deformed Poincare Invariance for Group Field Theories
• LQG propagator: III. The new vertex
• A Lagrangian approach to the Barrett-Crane spin foam model
• Spin Foam Quantization and Anomalies
• Super tensor models, super fuzzy spaces and super n-ary transformations
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• On the Implementation of the Canonical Quantum Simplicity Constraint
• Spin Foam Models of Matter Coupled to Gravity
• Group Field Theory in dimension four minus epsilon
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Tensor models and hierarchy of n-ary algebras
• Coupling gauge theory to spinfoam 3d quantum gravity
• The cubic matrix model and a duality between strings and loops
• Inhomogeneous universe from group field theory condensate
• Interpreting canonical tensor model in minisuperspace
• Positivity of Spin Foam Amplitudes
• Coherent states, constraint classes, and area operators in the new spin-foam models
• Quantum canonical tensor model and an exact wave function
• Generalised effective cosmology from group field theory
• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• An algebraic approach to coarse graining
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Spinors and Voros star-product for Group Field Theory: First Contact
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• Continuum spin foam model for 3d gravity
• The volume operator in covariant quantum gravity
• Generalised group field theories and quantum gravity transition amplitudes
• Dual variables and a connection picture for the Euclidean Barrett-Crane model
• Boundary terms in the Barrett-Crane spin foam model and consistent gluing
• Spin-Foam Models and the Physical Scalar Product
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Hamiltonian group field theory with multiple scalar matter fields
• Gauge fixing in the tensor model and emergence of local gauge symmetries
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Quantum Field Theory of Spin Networks
• Coarse graining in spin foam models
• The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• The lowest modes around Gaussian solutions of tensor models and the general relativity
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• q-Deformed spin foam models of quantum gravity
• The Construction of Spin Foam Vertex Amplitudes
• Frozen formalism and canonical quantization in group field theory
• Loop quantization from a lattice gauge theory perspective
• Loop Quantum Gravity's Boundary Maps
• A canonical rank-three tensor model with a scaling constraint
• Towards anisotropic cosmology in group field theory
• Tensor models and 3-ary algebras
• Quantum Gravity at the Turn of the Millennium
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Spinfoam 2d quantum gravity and discrete bundles
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• A Renormalizable SYK-type Tensor Field Theory
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• A More Sensitive Lorentzian State Sum
• Evaluation of new spin foam vertex amplitudes
• A renormalization procedure for tensor models and scalar-tensor theories of gravity
• Second-order amplitudes in loop quantum gravity
• Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
• Intertwiner Entanglement Excitation and Holonomy Operator
• Quantum gravity as a group field theory: a sketch
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Spin foams
• Spin foam quantization of SO(4) Plebanski's action
• Matrix model formulation of four dimensional gravity
• Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model
• Quantum Field Theory of Open Spin Networks and New Spin Foam Models
• Spin Network Wavefunction and the Graviton Propagator
• An $OSp$ extension of Canonical Tensor Model
• Aspects of quantum gravity
• Tensor and spin representations of SO(4) and discrete quantum gravity
• Hilbert space formalisms for group field theory
• Relating Spin Foams and Canonical Quantum Gravity: A Discrete Step Evolution Formulation of Spin Foams
• Reality Conditions for Spin Foams
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
• Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity
• Spin Foams for the Real, Complex Orthogonal Groups in 4D and the bivector scalar product reality constraint
• A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications
• Reconstructing the metric in group field theory
• Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms
• Spin Foam Models of Gravity and BF Theory as evolution of Spin Networks
• Simplicity condition and boundary-bulk duality
• Cosmological implications of the hydrodynamical phase of group field theory
• Thermofield Double States in Group Field Theory
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model
• Quartic Tensor Models
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
• Hessian in the spinfoam models with cosmological constant
• Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity
• 2d manifold-independent spinfoam theory