相关论文: Renormalization of an Abelian Tensor Group Field T…
A connection modulo gauge symmetry on the trivial principal bundle $M\times G$ is a morphism from the loop group of $M$ into $G$. Thus, considering only loops around the 2-cells of a distinguished family of progressively refined cellular…
The melonic limit is a relatively new type of large-$N$ limit, differing from the much older and well-known large-$N$ limits of vector and matrix field theories, which are dominated by cactus and planar Feynman diagrams, respectively. The…
These lecture notes give an introduction to the algebraic renormalization of the Standard Model. We start with the construction of the tree approximation and give the classical action and its defining symmetries in functional form. These…
We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken Abelian supersymmetric theory. We show that there exists (at least through three loops) a renormalisation group invariant trajectory for the coefficient of…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the category theory. We add the restriction on the…
A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and Maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…
Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We explore the renormalization group flow of quartic perturbations in the low-energy theory of graphene, in the strong Coulomb coupling and large-N limits, where N is the number of fermion flavors. We compute the anomalous dimensions of the…
For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved…
We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the $\phi^4 $ theory defined in $d=2$-dimension. We found a good agreement with the results obtained by the field-theoretical…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…
In this work we present an algebraic proof of the renormazibility of the super-Yang-Mills action quantized in a generalized supersymmetric version of the maximal Abelian gauge. The main point stated here is that the generalized gauge…
We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…