Bosonic Colored Group Field Theory

Abstract

Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman amplitudes in the "ultraspin" (large spin) limit. The results are generalized in any dimension. Finally integrating out two colors we write a new representation which could be useful for the constructive analysis of this type of models.

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Cited by in corpus (53)

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• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The Tensor Track, III
• Tensor models and embedded Riemann surfaces
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• EPRL/FK Group Field Theory
• Phase Transition in Dually Weighted Colored Tensor Models
• The Ising Model on Random Lattices in Arbitrary Dimensions
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• Invitation to Random Tensors
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• Functional Renormalization Group Approach for Tensorial Group Field Theory: A Rank-6 Model with Closure Constraint
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• Algebraic structures in quantum gravity
• Random Tensors and Quantum Gravity
• Bubbles and jackets: new scaling bounds in topological group field theories
• Bubble divergences: sorting out topology from cell structure
• A Deformed Poincare Invariance for Group Field Theories
• Constructive tensor field theory: The $T_4^4$ model
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• A Renormalizable 4-Dimensional Tensor Field Theory
• A simple proof of orientability in colored group field theory
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• The Construction of Spin Foam Vertex Amplitudes
• 3d Gravity as a random ensemble
• Renormalizable Tensor Field Theories
• Extending the Tutte and Bollobás-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
• Emergent matter from 3d generalised group field theories
• Ward-Takahashi identities for the colored Boulatov model
• Classical Group Field Theory
• Translation-Invariant Noncommutative Renormalization
• On the depth of quantum space
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• GEMs and amplitude bounds in the colored Boulatov model
• Polynomial Invariants for Arbitrary Rank $D$ Weakly-Colored Stranded Graphs
• Weighting bubbles in group field theory
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