Challenges of D=6 N=(1,1) SYM Theory

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to the N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses similar properties but is nonrenomalizable and serves as a toy model for supergravity. We consider the on-shell four point scattering amplitude and analyze its perturbative expansion within the spin-helicity and superspace formalism. The integrands of the resulting diagrams coincide with those of the N=4 D=4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions, no IR divergences on mass shell appear. We calculate analytically the leading logarithmic asymptotics in all loops. Their summation leads to a Regge trajectory which is calculated exactly. The leading powers of s are calculated up to six loops. Their summation is performed numerically and leads to a smooth function of s. The leading UV divergences are calculated up to 5 loops. The result suggests the geometrical progression which ends up in a finite expression. This leads us to a radical point of view on nonrenormalizable theories.Comment: 11 pages, 2 figures, Late

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

Политическая стабильность и нестабильность как элемент политической системы древневосточных государств (на примере Древнего Египта).

Власенко Д.И.Политическая стабильность и нестабильность как элемент политической системы древневосточных государств (на примере Древнего Египта). / Д.И.Власенко // Актуальні проблеми політики : зб. наук. пр. / редкол. : С. В. Ківалов (голов. ред.), Л. І. Кормич (заст. голов. ред.), Ю. П. Аленін [та ін.] ; МОНмолодьспорт України, НУ ОЮА. – Одеса : Фенікс, 2011. – Вип. 12-18 . С.294 - 305.In the work the questions connected with all aspects of a stable and unstable condition of political system of Ancient Egypt are considered. The expediency of studying of political system of Ancient Egypt proves, classifi cation of vari- ous conditions of political stability-instability is offered

Horizontal dispersion in shelf seas: High resolution modelling as an aid to sparse sampling

The ability of a hydrodynamic model to reproduce the results of a dye release experiment conducted in a wide shelf sea environment was investigated with the help of the Massachusetts Institute of Technology general circulation model (MITgcm). In the field experiment a fluorescent tracer, Rhodamine WT, was injected into the seasonal pycnocline, and its evolution was tracked for two days using a towed undulating vehicle equipped with a fluorometer and a CTD. With a 50. m horizontal resolution grid, and with three different forcings initialized in the model (viz: tides, stationary current, and wind stress on the free surface), it was possible to replicate the dye patch evolution quite accurately. The mechanisms responsible for the enhancement of horizontal dispersion were investigated on the basis of the model results. It was found that enhancement of the dye dispersion was controlled by vertically sheared currents that, in combination with vertical diapycnal mixing, led to a substantial increase in the "effective" horizontal mixing. The values of "effective" horizontal mixing found from the model runs were in good agreement with those obtained from in-situ data, and the probable degree to which the observational techniques undersampled the dye patch was revealed