Critical behavior of U(n)U(n)-χ4\chi^{4}-model with antisymmetric tensor order parameter coupled with magnetic field

The critical behavior of $U(n)$-$\chi^{4}$-model with antisymmetric tensor order parameter at charged regime is studied by means of the field theoretic renormalization group at the leading order of $\varepsilon$-expansion (one-loop approximation). It is shown that renormalization group equations have no infrared attractive charged fixed points. It is also shown that anomalous dimension of the order parameter in charged regime appears to be gauge dependent.Comment: 6 pages; the talk presented at 19th International Seminar on High Energy Physics "QUARKS-2016

Six loop analytical calculation of the field anomalous dimension and the critical exponent η\eta in O(n)O(n)-symmetric φ4\varphi^4 model

We report on a completely analytical calculation of the field anomalous dimension $\gamma_{\varphi}$ and the critical exponent $\eta$ for the $O(n)$-symmetric $\varphi^4$ model at the record six loop level. We successfully compare our result for $\gamma_{\varphi}$ with $n=1$ with the predictions based on the method of the Borel resummation combined with a conformal mapping. Predictions for seven loop contribution to the field anomalous dimensions are given.Comment: 16 page

Renormalization-group investigation of a superconducting U(r)U(r)-phase transition using five loops calculations

We have studied a Fermi system with attractive $U(r)$-symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for $r\geq 4$ the RG flux leaves the system's stability region -- the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. As the result this analysis shows that for $3D$ systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D=6,8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D=6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D=8,10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of (perturbation theory) PT. At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.Comment: 43 pages, 13 figures, pdf LaTex, v2 minor changes and references adde