Related papers: Renormalization Group Determination of the Five-Lo…
I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to…
I compute the complete two-loop effective potential for the minimal supersymmetric standard model in the Landau gauge. This enables an accurate determination of the minimization conditions for the vacuum expectation values of the Higgs…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension…
Through two loop effective potential we demonstrate that the $\bar{MS}$ scheme of dimensional regularization and Jackiw's prescription in cut-off regularization allow for the dynamical breaking solution in massless $\lambda\phi^4$ theory,…
The semi-analytical $O(\alpha_s^4)$ expression for 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 existing information…
We consider the effective potential V in the massless Wess-Zumino model. By using the renormalization group equation, we show that the explicit dependence of V on the renormalization mass scale mu cancels. If V has an extremum at some…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New…
The general structure of the renormalization group equations for the low energy effective field theory formulation of pure gravity is presented. The solution of these equations takes a particular simple form if the mass scale of the…
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.…
We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal…
The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method a characteristic scale $\mu_{s}$ is introduced to regularize the divergent…
The effective potential of quantized scalar field on fuzzy sphere is evaluated to the two-loop level. We see that one-loop potential behaves like that in the commutative sphere and the Coleman-Weinberg mechanism of the radiatively symmetry…
We employ projection operator techniques in Hilbert space to derive a continuous sequence of effective Hamiltonians which describe the dynamics on successively larger length scales. We show for the case of \phi^4 theory that the masses and…
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.…
We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally…
We renormalize various scalar field theories with a $\phi^n$ self interaction such as $n$ $=$ $5$, $7$ and $9$ in their respective critical dimensions which are non-integer. The renormalization group functions for the $O(N)$ symmetric…
Following previous work by one of the authors [M.V.Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93, 105043 (2016).], we develop a new approach to the renormalization group, where the effective…