Leading and subleading UV divergences in scattering amplitudes for D =8 N =1 SYM theory in all loops
Abstract
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D =8 N =1 supersymmetric Yang-Mills theory in the planar limit. This theory belongs to the class of maximally supersymmetric gauge theories and presumably possesses distinguished properties beyond perturbation theory. We obtain the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way staring from the one loop (for the leading poles) and two loop (for the subleading ones) diagrams. As a particular example where the recursive relations have a simple form we consider the ladder type diagrams. The all-loop summation of the leading and subleading divergences is performed with the help of the differential equations which are the generalization of the RG equations for nonrenormalizable theories. They have explicit solutions for the ladder type diagrams. We discuss the properties of the obtained solutions and interpretation of the results.
- Publication:
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Physical Review D
- Pub Date:
- February 2017
- DOI:
- 10.1103/PhysRevD.95.045006
- arXiv:
- arXiv:1603.05501
- Bibcode:
- 2017PhRvD..95d5006K
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- PdfLatex, 16 pages, 5 figures, supplementary Math file