Adrian Tanasa

The double scaling limit of random tensor models

A bstractTensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions D ≥ 3. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size N while tuning to criticality, which turns out to be summable in dimension less than six. This double scaling limit is here extended to arbitrary models. This is done by means of the Schwinger-Dyson equations, which generalize the loop equations of random matrix models, coupled to a double scale analysis of the cumulants.

Commutative limit of a renormalizable noncommutative model

Renormalizable 44 models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent naive commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the ultraviolet/infrared mixing in Feynman graphs at any order in perturbation theory.

Combinatorial Dyson-Schwinger equations in noncommutative field theory

We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles

Parametric representation of a translation-invariant renormalizable noncommutative model

B_+^\gamma

The multi-orientable random tensor model, a review

which allows us to write down the combinatorial Dyson-Schwinger equations for noncommutative quantum field theory. One- and two-loops examples are explicitly worked out.

Curing the UV/IR mixing for field theories with translation-invariant star products

We construct here the parametric representation of a translation-invariant renormalizable scalar model on the noncommutative Moyal space of even dimension D. This representation of the Feynman amplitudes is based on some integral form of the noncommutative propagator. All types of graphs (planar and non-planar) are analyzed. The role played by noncommutativity is explicitly shown. This parametric representation established allows us to calculate the power counting of the model. Furthermore, the space dimension D is just a parameter in the formulae obtained. This paves the road for the dimensional regularization of this noncommutative model.

Overview of the parametric representation of renormalizable non-commutative field theory

After its introduction (initially within a group eld theory framework) in A. Tanasa, J. Phys. A 45 (2012) 165401, the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the 1=N expansion and of the large N limit (N being the size of the tensor), the combinatorial analysis of the various terms of this expansion and nally,

Poincaré and sl(2) algebras of order 3

The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation-invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness, we compute the form of the new action in the matrix base for the Wick-Voros product.

Algebraic structures in quantum gravity

We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.

Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach

In this paper, we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on sl(2,C) and iso(1, 3) the Poincare algebra in four dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.