Related papers: General Four-Loop Beta Function for Scalar-Fermion…
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous…
Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite volume,…
We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero in the beta function at $\alpha_{IR}$. We present general formulas for…
The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in ${\cal N}=4$ SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling…
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…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
We study the 3-point functions of single-trace scalar operators in a four-dimensional $\mathcal{N}=2$ SYM theory with gauge group $\mathrm{SU}(N)$ and matter in the symmetric plus anti-symmetric representation, which has a vanishing…
We study regularization scheme dependence of K\"ahler ($N=2$) supersymmetric sigma models. At the one-loop order the metric $\beta$ function is the same as in non-supersymmetric case and coincides with the Ricci tensor. First correction in…
We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space…
We unveil the general features of the phase diagram for any gauge theory with fermions transforming according to distinct representations of the underlying gauge group, at the four-loop order. We classify and analyze the zeros of 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…
The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the $\bt$-functions are calculated…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
The paper studies the quantum action for the four-dimensional real $\phi^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization…
We study the noncommutative $\phi^4$ theory with spontaneously broken global O(2) symmetry in 4 dimensions. We demonstrate the renormalizability at one loop. This does not require any choice of ordering of the fields in the interaction…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
Using differential renormalization, we calculate the complete two-point function of the background gauge superfield in pure N=1 Supersymmetric Yang-Mills theory to two loops. Ultraviolet and (off-shell) infrared divergences are renormalized…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$, and this…
We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell…