Related papers: Towards the five-loop Beta function for a general …
The beta function of the vacuum energy density is analytically computed at the five-loop level in O(N)-symmetric phi^4 theory, using dimensional regularization in conjunction with the MSbar scheme. The result for the case of a cubic…
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for…
We start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known beta function of Novikov et…
For a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the $\beta$-function defined in terms of the bare couplings is given by integrals of double total derivatives…
In the talk the leading four-loop contribution to the beta-function of the strong coupling in the SM is discussed. Some details of calculation techniques are provided. Special attention is paid to the ambiguity due to utilized $\gamma_5$…
We present the full expressions for the QCD beta-function in the MOMggg, MOMq and MOMh renormalization schemes at three loops for an arbitrary colour group in the Landau gauge. The results for all three schemes are in very good agreement…
We compute the one-loop effective action in \N=1 conformal SU(N) gauge theory which is an exactly marginal deformation of the \N=4 SYM theory. We consider an abelian background of constant \N = 1 gauge field and single chiral scalar. While…
The semi-analytical expression for the forth coefficient of the renormalization group $\beta$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the three-loop…
We discuss the current status of the investigations of the conformal symmetry breaking contributions to three forms for the QCD generalizations of the Crewther relation. The new third form of the extension of this relation is considered in…
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…
In ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives we obtain the four-loop beta function using a method based on calculating vacuum supergraphs. For this purpose we use a special C++ program which obtain contributions…
We calculate the three loop contribution to the beta-function of the gauge coupling constant in a general, anomaly-free, renormalisable gauge field theory involving a single gauge coupling using the background field method in the MSbar…
We discuss an analog of the AGT relation in five dimensions. We define a q-deformation of the beta-ensemble which satisfies q-W constraint. We also show a relation with the Nekrasov partition function of 5D SU(N) gauge theory with N_f=2N.
We study the impact of the Yukawa interaction in the large-$N_f$ limit to the abelian gauge theory. We compute the coupled $\beta$-functions for the system in a closed form at $\mathcal{O}(1/N_f)$.
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
We present the supersymmetric standard model three-loop $\beta$-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.
We take the manifestly gauge invariant exact renormalisation group previously used to compute the one-loop beta function in SU(N) Yang-Mills without gauge fixing, and generalise it so that it can be renormalised straightforwardly at any…
We study the three-loop gauge $\beta$-functions in general $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of…
We report about the computation of three-loop corrections to the gauge coupling beta functions in the Standard Model.
We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the…