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 TMF, 2017, Volume 192, Number 1, Pages 89–102 (Mi tmf9280)

Ultraviolet divergences in $D=8$ $N=1$ supersymmetric Yang–Mills theory

D. I. Kazakovab, D. E. Vlasenkoc

a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Moscow Oblast, Russia
c Physics Faculty, Southern Federal University, Rostov-on-Don, Russia

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.

Keywords: amplitude, maximal supersymmetry, UV divergence.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-02-0087217-0232-00837 This research was supported by by the Russian Foundation for Basic Research (Grant Nos. 14-02-00494 and 17-0232-00837).

DOI: https://doi.org/10.4213/tmf9280

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English version:
Theoretical and Mathematical Physics, 2017, 192:1, 1016–1027

Citation: D. I. Kazakov, D. E. Vlasenko, “Ultraviolet divergences in $D=8$ $N=1$ supersymmetric Yang–Mills theory”, TMF, 192:1 (2017), 89–102; Theoret. and Math. Phys., 192:1 (2017), 1016–1027

Citation in format AMSBIB
\Bibitem{KazVla17}
\by D.~I.~Kazakov, D.~E.~Vlasenko
\paper Ultraviolet divergences in $D=8$ $N=1$ supersymmetric Yang--Mills
theory
\jour TMF
\yr 2017
\vol 192
\issue 1
\pages 89--102
\mathnet{http://mi.mathnet.ru/tmf9280}
\crossref{https://doi.org/10.4213/tmf9280}
\elib{http://elibrary.ru/item.asp?id=29438858}
\transl
\jour Theoret. and Math. Phys.
\yr 2017
\vol 192
\issue 1
\pages 1016--1027
\crossref{https://doi.org/10.1134/S0040577917070066}