Joseph Ben Geloun

Bosonic colored group field theory

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.

Linearized Group Field Theory and Power Counting Theorems

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We prove exact power-counting theorems for any graph of such models. For linearized colored models the power counting of any amplitude is further computed in terms of the homology of the graph. An exact power-counting theorem is also established for a particular class of graphs of the nonlinearized models, which satisfy a planarity condition. Examples and connections with previous results are discussed.

Radiative Corrections in the Boulatov-Ooguri Tensor Model: The 2-Point Function

The Boulatov-Ooguri tensor model generates a sum over spacetime topologies for the D-dimensional BF theory. We study here the quantum corrections to the propagator of the theory. In particular, we find that the radiative corrections at the second order in the coupling constant yield a mass renormalization. They also exhibit a divergence which cannot be balanced with a counter-term in the initial action, and which usually corresponds to the wave-function renormalization.

3D Tensor Field Theory: Renormalization and One-Loop β-Functions

We prove that the rank 3 analogue of the tensor model defined in Ben Geloun and Rivasseau (Commun Math Phys, arXiv:1111.4997 [hep-th], 2012) is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop γ- and β-functions of the model are also determined. We find that the model with a unique coupling constant for all interactions and a unique wave-function renormalization is asymptotically free in the UV.

Two- and four-loop β-functions of rank-4 renormalizable tensor field theories

A recent rank 4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory [arXiv:1111.4997 [hep-th]]. The model is built out of

Some classes of renormalizable tensor models

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Counting Tensor Model Observables and Branched Covers of the 2-Sphere

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Addendum to: A Renormalizable 4-Dimensional Tensor Field Theory

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Tensor models, Kronecker coefficients and permutation centralizer algebras

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On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov–Ooguri models

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