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 sypersymmetric Yang-Mills theory within the spinor-helicity and superfield formalism. 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 non-renormalizable theories. They have explicit solutions for the ladder type diagrams. We discuss the properties of the obtained solutions and interpretation of the results.

PdfLatex, 16 pages, 5 figures, supplementary Math file

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• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
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Cited by in corpus (7)

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• Quasi-Renormalizable Quantum Field Theories
• High Energy Behaviour in Maximally Supersymmetric Gauge Theories in Various Dimensions
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs