Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models

Abstract

In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra whose quantum geometry is encoded in non-local degrees of freedom on the non-compact group $\mathrm{SL}(2,\mathbb{C})$ and subject to gauge and simplicity constraints. Further we include $\mathbb{R}$-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.

arXiv comment41 + 20 pages, 2 figures; matches published version

References in corpus (90)

• Background Independent Quantum Gravity: A Status Report
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• 2D Gravity and Random Matrices
• Loop Quantum Cosmology: A Status Report
• The Spin Foam Approach to Quantum Gravity
• The nonperturbative functional renormalization group and its applications
• Spin Foam Models for Quantum Gravity
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Critical behavior of colored tensor models in the large N limit
• Topological Lattice Models in Four Dimensions
• Nonperturbative Quantum Gravity
• Partial observables
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Group Field Theory: An overview
• Partial and Complete Observables for Canonical General Relativity
• A Lorentzian Signature Model for Quantum General Relativity
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• 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
• The causal set approach to quantum gravity
• Quantum Graphity: a model of emergent locality
• Group field theory with non-commutative metric variables
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• Homogeneous cosmologies as group field theory condensates
• Melons are branched polymers
• Scalar Material Reference Systems and Loop Quantum Gravity
• Topological Graph Polynomials in Colored Group Field Theory
• Focusing on the Fixed Point of 4D Simplicial Gravity
• A generalization of the Virasoro algebra to arbitrary dimensions
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Spin foam model for Lorentzian General Relativity
• The universe as a quantum gravity condensate
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Bouncing cosmologies from quantum gravity condensates
• Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Lost in Translation: Topological Singularities in Group Field Theory
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Phase Structure of Four Dimensional Simplicial Quantum Gravity
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Lattice Quantum Gravity and Asymptotic Safety
• 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
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• 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
• Quantization maps, algebra representation and non-commutative Fourier transform for Lie groups
• 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
• A spin foam model for general Lorentzian 4-geometries
• Causal Dynamical Triangulations without Preferred Foliation
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• 3+1 spinfoam model of quantum gravity with spacelike and timelike components
• Newton-Cartan Gravity and Torsion
• Boosting Wigner's nj-symbols
• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Group field theory condensate cosmology: An appetizer
• Group field theory for quantum gravity minimally coupled to a scalar field
• Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• Group field theory formulation of 3d quantum gravity coupled to matter fields
• Why are tensor field theories asymptotically free?
• Effective relational cosmological dynamics from Quantum Gravity
• Group field theory and its cosmology in a matter reference frame
• Effective Hamiltonian Constraint from Group Field Theory
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Spin foams with timelike surfaces
• A Primer of Group Theory for Loop Quantum Gravity and Spin-foams
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• A Note on analytic formulas of Feynman propagators in position space
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• The Complete Barrett-Crane Model and its Causal Structure
• Phase transitions in group field theory: The Landau perspective
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Towards background independent quantum gravity with tensor models
• Inequivalent coherent state representations in group field theory
• (No) phase transition in tensorial group field theory
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Locally Causal Dynamical Triangulations in Two Dimensions
• Flowing in discrete gravity models and Ward identities: A review
• Non-commutative Fourier transform for the Lorentz group via the Duflo map
• Minimizers of the dynamical Boulatov model
• Non-relativistic limit of gravity theories in the first order formalism
• Topology induced first-order phase transitions in lattice quantum gravity
• A Wick rotation for EPRL spin foam models

Cited by in corpus (9)

• Mean-field phase transitions in TGFT quantum gravity
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Relational dynamics and Page-Wootters formalism in group field theory
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model