Journal of High Energy Physics

, 2015:59 | Cite as

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

  • L. V. Bork
  • D. I. Kazakov
  • M. V. Kompaniets
  • D. M. Tolkachev
  • D. E. Vlasenko
Open Access
Regular Article - Theoretical Physics


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.


Scattering Amplitudes Field Theories in Higher Dimensions Extended Supersymmetry Renormalization Group 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • L. V. Bork
    • 2
    • 4
  • D. I. Kazakov
    • 1
    • 2
    • 3
  • M. V. Kompaniets
    • 5
  • D. M. Tolkachev
    • 1
    • 7
  • D. E. Vlasenko
    • 1
    • 6
  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Alikhanov Institute for Theoretical and Experimental PhysicsMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  4. 4.Center for Fundamental and Applied ResearchAll-Russian Institute of AutomaticsMoscowRussia
  5. 5.St. Petersburg State UniversitySt. PetersburgRussia
  6. 6.Department of PhysicsSouthern Federal State UniversityRostov-DonRussia
  7. 7.Department of PhysicsGomel State UniversityGomelBelarus

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