All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory

TL;DR

This paper computes all non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, providing new results and insights into their structure and properties, including partial results for higher-point amplitudes and twistor-space characteristics.

Contribution

It presents the first complete calculation of non-MHV seven-gluon one-loop amplitudes in N=4 SYM and introduces new coefficients and twistor-space analyses for these amplitudes.

Findings

All independent one-loop seven-gluon helicity amplitudes are now known.

Partial results for an infinite sequence of next-to-MHV amplitudes are provided.

Twistor-space properties of the amplitude coefficients are simple and suggestive.

Abstract

We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n-3 positive-helicity gluons, and the color ordering (- - - + + ... + +); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.