Related papers: One-loop $\beta$ functions of a translation-invari…
We compute the one-loop \beta-functions describing the renormalisation of the coupling constant \lambda and the frequency parameter \Omega for the real four-dimensional duality-covariant noncommutative \phi^4-model, which is renormalisable…
In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established.…
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 $\phi^6$ ($\phi^6_{(1/2)}$), $\phi^4$…
The simplest non commutative renormalizable field theory, the $\phi_4^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this result up to…
The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using…
We make here a short overview of the recent developments regarding translation-invariant models on the noncommutative Moyal space. A scalar model was first proposed and proved renormalizable. Its one-loop renormalization group flow and…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this…
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.…
We show that gauge-independent terms in the one-loop and multi-loops $\beta$-functions of the Standard Model can be exactly computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite…
We study the $\frac{\lambda}{4!}\phi^{4}$ massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking…
Within the context of massive N-component $\phi^4$ scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
We study the two-dimensional version of a quartic self-interacting quantum scalar field on a curved and noncommutative space (Snyder-de Sitter). We show that the model is renormalizable at the one-loop level and compute the beta functions…
We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $\overline{MS}$-scheme. We do not explicitly compute relevant loop integrals but utilize…
Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambda phi^4 model with external source and without mass and they have clarified that there are underlying renormalization group structure, including the phenomenon of the…
Renormalizable $\phi^{\star 4}_4$ 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…
We prove that the rank 3 analogue of the tensor model defined in [arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop $\gamma$- and $\beta$-functions of the model…
We perform a detailed analysis of renormalization at one-loop order in the $\lambda\phi^4$ theory with Robin boundary condition (characterized by a constant $c$) on a single plate at $z=0$. For arbitrary $c\geq0$ the renormalized theory is…