On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity

TL;DR

This paper investigates the singularities of higher-loop scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity, providing a physical interpretation and simplifying computational techniques through pictorial methods.

Contribution

It introduces a new interpretation of singularities in complex integrals, clarifies the rung-rule and correction integrals, and links unphysical singularities to dual conformal invariance.

Findings

Singularities can be understood physically and pictorially.

Corrections to the rung-rule cancel unphysical singularities.

Unphysical singularities relate to conformal cross-ratios and dual conformal invariance.

Abstract

Exploiting singularities in Feynman integrals to get information about scattering amplitudes has been particularly useful at one-loop in theories where no triangles or bubbles appear. At higher loops the integrals possess subtle singularities. In this paper we give these singularities a physical interpretation and show how they turn tedious computations into purely pictorial manipulations. We illustrate our methods with various examples from the computation of four-particle amplitudes in N=4 super Yang-Mills and N=8 supergravity. Along the way we find clues towards an understanding i) of the rung-rule as a consequence of infra-red singularities, ii) of the non rung-rule integrals included in the basis as corrections to the rung-rule and iii) of the coefficients - including signs - of these two types of contribution. The role of corrections is to cancel unphysical singularities generically present in rung-rule integrals. A further byproduct, coming from the fact such unphysical singularities are located where conformal cross-ratios become unity, is the possibility of understanding the dual conformal invariance ansatz for constructing the basis of four-particle amplitudes in N=4 super Yang-Mills.