Related papers: A Perspective on Regularization and Curvature
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $ \beta $-functions are known to the 3-2-2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
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…
Renormalization schemes and cutoff schemes allow for the introduction of various distinct renormalization scales for distinct couplings. We consider the coupled renormalization group flow of several marginal couplings which depend on just…
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV)…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories is investigated in the case of using the regularization by higher covariant derivatives. It is demonstrated that this regularization allows revealing some…
We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them…
At present, the gauge coupling $\beta$-function in the Standard Model (SM) is known up to four-loop order. As most SM calculations, dimensional regularization was employed. Despite its striking success, other regularization schemes have…
The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the \beta functions of parameters with and without a mass dimension.