Leading and Subleading UV Divergences in Scattering Amplitudes for D=8 N=1 SYM Theory in All Loops

TL;DR

This paper analyzes the ultraviolet divergences in four-point scattering amplitudes of D=8 N=1 supersymmetric Yang-Mills theory, deriving recursive relations and summing divergences across all loops for specific diagram types.

Contribution

It introduces recursive relations for all-loop divergences in D=8 N=1 SYM and provides explicit solutions for ladder diagrams using generalized RG equations.

Findings

Recursive relations for divergences at all loops.

Explicit all-loop solutions for ladder diagrams.

Insights into the properties of divergences in non-renormalizable theories.

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.