Related papers: Geometrically relating momentum cut-off and dimens…
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 consider Lifshitz-type scalar theories with explicit breaking of the Lorentz symmetry that, in addition, exhibit anisotropic scaling laws near the ultraviolet fixed point. Using the proper time regularization method on the spatial…
We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $\gamma_5$ in $D=4-2\epsilon$ space-time dimensions is required;…
We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without St\"uckelberg…
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 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…
The two-loop anomalous dimension of the chiral matter superfields is calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of…
The idea of reduction of couplings in renormalizable theories will be presented and then will be applied in Particle Physics models. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group…
We study the relationship between the renormalization group and the diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed…
The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
The standard formulation of a massive Abelian vector field in $2+1$ dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term. In this latter…
We verify a recently proposed method for obtaining a $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $\beta$-function can be found by…
We analyze the behavior of several renormalization group functions at infrared fixed points for $SU(N)$ gauge theories with fermions in the fundamental and two-indexed representations. This includes the beta function of the gauge coupling,…
$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and…
I compare heatkernel regularization with sharp gauge invariant cutoffs in the Hamiltonian formulation of the Coulomb gauged Schwinger model on a circle. The effective potential for the zero mode of the gauge field in a given fermionic…
In this work, we study the renormalization-group evolution of parameters in the three-dimensional effective field theory (3D EFT) that describes the thermally driven electroweak phase transition of the Higgs field. We consider tree-level…
We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional $\sigma$ model it is demonstrated that the background-field method gives…
A momentum dependent projection of the Wegner-Hougton equation is derived for a scalar theory coupled to an external field. This formalism is useful to discuss the phase diagram of the theory. In particular we study some properties of the…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…