Light-by-Light Scattering Effect in Light-Cone Supergraphs

TL;DR

This paper explains the UV finiteness predictions for maximally supersymmetric theories using light-cone supergraph properties, linking dynamical supersymmetry to light-by-light scattering effects similar to QED.

Contribution

It provides a simple explanation for the UV properties of supersymmetric theories based on light-cone supergraph analysis and dynamical supersymmetry considerations.

Findings

N=4 super Yang-Mills is UV finite.

N=8 supergravity is UV finite until at least 7 loops.

n-point amplitudes have no UV divergences until at least n+3 loops.

Abstract

We give a relatively simple explanation of the light-cone supergraph prediction for the UV properties of the maximally supersymmetric theories. It is based on the existence of a dynamical supersymmetry which is not manifest in the light-cone supergraphs. It suggests that N=4 supersymmetric Yang-Mills theory is UV finite and N=8 supergravity is UV finite at least until 7 loops whereas the $n$-point amplitudes have no UV divergences at least until $L=n+3$. Here we show that this prediction can be deduced from the properties of light-cone supergraphs analogous to the light-by-light scattering effect in QED. A technical aspect of the argument relies on the observation that the dynamical supersymmetry action is, in fact, a compensating field-dependent gauge transformation required for the retaining the light-cone gauge condition $A_+=0$.