Summation of all-loop UV Divergences in Maximally Supersymmetric Gauge Theories

TL;DR

This paper analyzes the all-loop UV divergences in maximally supersymmetric gauge theories in various dimensions, providing recursive relations and differential equations to sum divergences and interpret their properties.

Contribution

It introduces algebraic recursive relations and differential equations to sum all-loop UV divergences in maximally supersymmetric gauge theories.

Findings

Derived recursive relations for divergences at all loops

Solved differential equations generalizing RG equations

Analyzed properties and interpretations of the solutions

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.