Abstract
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in the D=8 N=1 supersymmetric Yang–Mills theory in the planar limit for ladder-type diagrams. We obtain recurrence relations that allow obtaining the leading and subleading divergences in all loops purely algebraically starting from the one-loop diagrams (for the leading poles) and the two-loop diagrams (for the subleading poles). We sum the leading and subleading divergences over all loops using differential equations that are generalizations of the renormalization group equations to nonrenormalizable theories. We discuss the properties of the obtained solutions and the dependence of the constructed counterterms on the scheme.
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Dedicated to D. V. Shirkov
This research was supported by the Russian Foundation for Basic Research (Grant Nos. 14-02-00494 and 17-0232-00837).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 1, pp. 89–102, July, 2017.
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Kazakov, D.I., Vlasenko, D.E. Ultraviolet divergences in D=8 N=1 supersymmetric Yang–Mills theory. Theor Math Phys 192, 1016–1027 (2017). https://doi.org/10.1134/S0040577917070066
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DOI: https://doi.org/10.1134/S0040577917070066