Related papers: Towards the five-loop Beta function for a general …
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…
We present the results for three-loop beta-functions for Yukawa couplings of heavy Standard Model fermions calculated within the unbroken phase of the model. The calculation is carried out with the help of the MINCER program in a general…
We develop the necessary tools for computing fluctuations around a mean-field background in the context of SU(N) lattice gauge theories in five dimensions. In particular, expressions for the scalar observable and the Wilson Loop are given.…
We consider vectorial, asymptotically free ${\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of…
We present the full three-loop beta-functions for the MSSM generalised to include additional matter multiplets in 5, 10 representations of SU(5). We analyse in detail the effect of three-loop running on the sparticle spectrum for the MSSM…
We calculate the $\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring…
We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…
We calculate the two-loop renormalization group equations for the running gaugino masses in general SUSY gauge models, improving our previous result. We also study its consequence to the unification of the gaugino masses in the SUSY SU(5)…
A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the large N limit. In this way we make precise and concrete the notion of a non-perturbative gauge invariant…
The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than…
Using a gauge invariant exact renormalization group, we show how to compute the effective action, and extract the physics, whilst manifestly preserving gauge invariance at each and every step. As an example we give an elegant computation of…
We present calculations of the leading and $O(1/N_f)$ terms in a large-$N_f$ expansion of the $\beta$-functions and anomalous dimensions for various supersymmetric gauge theories, including supersymmetric QCD. In the case of supersymmetric…
The contributions of the matter superfields and of the Faddeev--Popov ghosts to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the…
We study the gauge transformation of the recently computed one-loop four-point function of {\cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). The contributions from nonplanar diagrams are not gauge invariant. We compute…
The Penner type beta-ensemble for Omega-deformed N=2 SU(2) gauge theory with two massless flavors arising as a limiting case from the AGT conjecture is considered. The partition function can be calculated perturbatively in a saddle-point…
We clarify the mass dependence of the effective prepotential in N=2 supersymmetric SU(N_c) gauge theories with an arbitrary number N_f<2N_c of flavors. The resulting differential equation for the prepotential extends the equations obtained…
We have extended our previous computations, performed analytically for a general gauge group, of the even-$N$ moments $\gamma_{\rm ik}^{\,(3)}(N)$ of the four-loop flavour-singlet splitting functions $P_{\rm ik}^{\,(3)}(x)$ to $N = 22$. The…
We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $\beta$ functions of these theories are…
We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…