Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

被引：0
作者：
L. V. Bork
D. I. Kazakov
M. V. Kompaniets
D. M. Tolkachev
D. E. Vlasenko
机构：
[1] Joint Institute for Nuclear Research,Bogoliubov Laboratory of Theoretical Physics
[2] Alikhanov Institute for Theoretical and Experimental Physics,Center for Fundamental and Applied Research
[3] Moscow Institute of Physics and Technology,Department of Physics
[4] All-Russian Institute of Automatics,Department of Physics
[5] St. Petersburg State University,undefined
[6] Southern Federal State University,undefined
[7] Gomel State University,undefined
来源：
Journal of High Energy Physics | / 2015卷
关键词：
Scattering Amplitudes; Field Theories in Higher Dimensions; Extended Supersymmetry; Renormalization Group;
D O I：
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摘要：
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.
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