Minimizers of the dynamical Boulatov model

Abstract

We study the Euler-Lagrange equation of the dynamical Boulatov model which is a simplicial model for 3d Euclidean quantum gravity augmented by a Laplace-Beltrami operator. We provide all its solutions on the space of left and right invariant functions that render the interaction of the model an equilateral tetrahedron. Surprisingly, for a non-linear equation of motion, the solution space forms a vector space. This space distinguishes three classes of solutions: saddle points, global and local minima of the action. Our analysis shows that there exists one parameter region of coupling constants for which the action admits degenerate global minima.

arXiv commentclosest to published version

References in corpus (29)

• A Model of Three-Dimensional Lattice Gravity
• Dynamically Triangulating Lorentzian Quantum Gravity
• Group Field Theory: An overview
• Colored Group Field Theory
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• Homogeneous cosmologies as group field theory condensates
• Group field theory renormalization - the 3d case: power counting of divergences
• The Ponzano-Regge model
• Scaling behaviour of three-dimensional group field theory
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Bouncing cosmologies from quantum gravity condensates
• Lost in Translation: Topological Singularities in Group Field Theory
• Flowing in Group Field Theory Space: a Review
• Non-perturbative summation over 3D discrete topologies
• Invitation to Random Tensors
• Non-perturbative thermal flows and resummations
• 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
• Quantum Gravity via Causal Dynamical Triangulations
• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Quantum cosmology of (loop) quantum gravity condensates: An example
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Relational evolution of effectively interacting GFT quantum gravity condensates
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Convexity of the effective action from functional flows
• Inequivalent coherent state representations in group field theory
• The Ponzano-Regge asymptotic of the 6j symbol: an elementary proof
• The group field theory approach to quantum gravity

Cited by in corpus (7)

• Group field theory condensate cosmology: An appetizer
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Aspects of quantum gravity