The property of maximal transcendentality of anomalous dimensions of the Wilson operators in the <Emphasis Type="Italic">N</Emphasis> = 4 SYM

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

Anomalous dimensions of the Wilson operators in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory. The text was submitted by the authors in English.     

Strong-coupling constant with flavor thresholds at five loops in the modified minimal-subtraction scheme

We present in analytic form the matching conditions for the strong-coupling constant alphas(nf) (mu) at the flavor thresholds to four loops in the modified minimal-subtraction scheme. Taking into account the present knowledge on the coefficient beta4 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a five-loop formula for alphas(nf) (mu) together with appropriate relationships between the asymptotic scale parameters Lamda(nf) for different numbers of flavors nf.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations

We briefly review the uniqueness method, which is a powerful technique for calculating multiloop Feynman diagrams in theories with conformal symmetries. We use the method in the momentum space and show its effectiveness in calculating a two-loop massless propagator Feynman diagram with a noninteger index on the central line. We use the obtained result to compute the optical conductivity of graphene at the infrared Lorentz-invariant fixed point. We analyze the effect of counterterms and compare with the nonrelativistic limit.     

Landau–Khalatnikov–Fradkin Transformation and Even $$\zeta$$ Functions

Physics of Atomic Nuclei - An exact formula that relates standard $$\zeta$$ functions and so-called hatted $$\zeta$$ ( $$\hat{\zeta}$$ ) functions in all orders of perturbation theory is presented....     

Counting master integrals: Integration-by-parts procedure with effective mass

We show that the new relation between master integrals recently obtained in M.Yu. Kalmykov and B.A. Kniehl (2011) [1] can be reproduced using the integration-by-parts technique implemented with an effective mass. In fact, this relation is recovered as a special case of a whole family of new relations between master integrals.     

Analytic solution of the multiloop Baxter equation

The asymptotic spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang–Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2)$sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their asymptotic anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.