Abstract
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results.
Highlights
Within the dimensional regularization the UV divergences manifest themselves as the pole terms with the numerators being the polynomials over the kinematic variables
The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories
In recent papers [15,16,17], we considered the leading and subleading UV divergences of the on-shell scattering amplitudes for all three cases of maximally supersymmetric SYM theories, D=6 (N=2 SUSY), D=8 (N=1 SUSY) and D=10 (N=1 SUSY)
Summary
We start with the leading poles and calculate them in all loops. This is possible even in the non-renormalizable case due to the structure of the UV divergences, which follows from the R -operation. The procedure is based on the consistent application of the R -operation and integration over the remaining triangle and bubble diagrams with the help of Feynman parameters These relations take into account all the diagrams of a given order of PT and allow one to calculate the leading poles taking the one-loop one as input but to sum all orders of PT. For the ladder type diagrams the remained integration over Feynman parameters can be performed explicitly and one is left with the algebraic (for recursive relations) or ordinary differential equations (for the sum of diagrams), which can be explicitly solved.
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