Generalising holographic fishchain

In this paper we present an attempt to generalise the integrable Gromov-Sever models, the so-called fishchain models, which are dual to biscalar fishnets. We show that in any dimension they can be derived at least for some integer deformation parameter of the fishnet lattice and also for the triscalar models. We focus in particular on the study of fishchain models in AdS$_7$ that are dual to the six-dimensional fishnet models.Comment: 20 pages, 2 figure

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

Leading all-loop quantum contribution to the effective potential in general scalar field theory

The RG equation for the effective potential in the leading log (LL) approximation is constructed which is valid for an arbitrary scalar field theory in 4 dimensions. The solution to this equation sums up the leading log\phi contributions to all orders of perturbation theory. In general, this is the second order nonlinear partial differential equation, but in some cases it can be reduced to the ordinary one. For particular examples, this equation is solved numerically and the LL effective potential is constructed. The solution has a characteristic discontinuity replacing the Landau pole typical for the phi^4 theory. For a power-like potential no new minima appear due to the Coleman-Weinberg mechanismComment: 13 pages, 10 figures, Late

Leading all-loop quantum contribution to the effective potential in the inflationary cosmology

In this paper, we have constructed quantum effective potentials and used them to study slow-roll inflationary cosmology. We derived the generalised RG equation for the effective potential in the leading logarithmic approximation and applied it to evaluate the potentials of the $T^2$ and $T^4$-models, which are often used in modern models of slow-roll inflation. We found that while the one-loop correction strongly affects the potential, breaking its original symmetry, the contribution of higher loops smoothes the behaviour of the potential. However, unlike the $\phi^4$-case, we found that the effective potentials preserve spontaneous symmetry breaking when summing all the leading corrections. We calculated the spectral indices $n_s$ and $r$ for the effective potentials of both models and found that they are consistent with the observational data for a wide range of parameters of the models.Comment: 15 pages, 6 figure

Summation of all-loop UV divergences in maximally supersymmetric gauge theories

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results.Comment: PdfLatex, 18 pages, 9 Figure