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

TL;DR

The paper analyzes the UV properties of maximal supersymmetric theories through the lens of light-cone supergraphs, showing that dynamical supersymmetry acts as a compensating field-dependent gauge transformation once the gauge ${A_+ = 0}$ is fixed. This viewpoint explains why UV divergences depend on field strengths rather than potentials, yielding an improved UV behavior: ${\cal N}=4$ SYM remains UV finite and ${\cal N}=8$ SUGRA remains UV finite at least up to $7$ loops, with $n$-point amplitudes free of divergences up to loop order $L=n+3$. The mechanism hinges on the requirement of transverse-m momentum factors per external leg, effectively mimicking a light-by-light scattering scenario in the light-cone supergraphs, and ties the finiteness to the interplay between dynamical SUSY and gauge symmetry. The discussion also considers the role of hidden non-linear symmetries such as $E_{7(7)}$ in potentially shaping all-loop finiteness and outlines directions for future work to understand these symmetries’ impact on the UV structure.

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 $A_+=0$.