The Sachdev-Ye-Kitaev (SYK) model is a of q interacting fermions. Gross and Rosenhaus have proposed generalization the SYK which involves fermions with different flavors. In terms Feynman graphs, those flavors are reminiscent colors used in random tensor theory. This gives us opportunity to apply some modern, yet elementary, tools developed context tensors one particular instance such colored models. We illustrate our method by identifying all diagrams contribute leading next-to-leading...

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs tensor generalizing ribbon (or combinatorial maps); these dual not only to manifolds. In order simplify the topological structure various singularities, colored was recently introduced and intensively studied since. We propose here different simplification GFT, which we call multi-orientable GFT. study relation between colorable graphs. prove...

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

In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that does not suffer from UV/IR mixing and establish its renormalizability to all orders in perturbation theory.

We investigate the relationship between universal topological polynomials for graphs in mathematics and parametric representation of Feynman amplitudes quantum field theory. In this first article we consider translation invariant theories with usual heat-kernel-based propagator. show how Symanzik theory are particular multivariate versions Tutte polynomial, new noncommutative special Bollobás–Riordan polynomials.

We introduce here the Hopf algebra structure describing noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. define Hochschild one-cocyles B_+^\gamma which allows us to write down combinatorial Dyson–Schwinger equations for quantum field theory. One- and two-loops examples are explicitly worked out.

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated graphs, or 3D maps, can be classified with respect to particular integer half-integer, degree respective graph. In this paper we analyze general term asymptotic expansion in N, size tensor, model, multi-orientable model. We perform their enumeration and establish which dominant configurations given degree.

We contruct here the Hopf algebra structure underlying process of renormalization non-commutative quantum field theory.

We investigate the group field theory formulation of Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK spin-foam models. These models aim at a dynamical, i.e., nontopological 4D quantum gravity. introduce saddle point method for general amplitudes and compare it with existing results, in particular, second order correction to EPRL/FK propagator.

In this paper we study the double scaling limit of multi-orientable tensor model.We prove that, contrary to case matrix models but similarly invariant models, series are convergent.We resum two point function and leading singular part four function.We discuss behavior arbitrary correlation functions.We show that contribution all higher functions enhanced in limit.We finally exhibit a singularity at same critical value parameter which, combined with convergence series, suggest existence triple limit.

We study the effect of non-Gaussian average over random couplings in a complex version celebrated Sachdev-Ye-Kitaev (SYK) model. Using Polchinski-like equation and tensor Gaussian universality, we show that this averaging leads to modification variance distribution at leading order $N$. then derive form effective action all orders. An explicit computation case quartic perturbation is performed for both SYK model mentioned above generalization proposed D. Gross V. Rosenhaus [J. High Energy...

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

Starting from a recently-introduced algebraic structure on spin foam models, we define Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for mirror analysis of models quantum field theory, combinatorial point view. A grafting operator is introduced allowing the equivalent Dyson-Schwinger equation to be written. Non-trivial examples are explicitly worked out. Finally, physical significance results discussed.

This paper is devoted to the study of renormalization quartic melonic tensor model in dimension (=rank) five. We review perturbative and computation one loop beta function, confirming asymptotic freedom model. then define Connes-Kreimer-like Hopf algebra describing combinatorics this we analyze detail, at one- two-loop levels, Hochschild cohomology allowing write combinatorial Dyson-Schwinger equations. Feynman graph subalgebras are also exhibited.