One-Loop Self-Dual and N=4 Super Yang-Mills

TL;DR

This paper proposes a conjectural relationship between one-loop gluon amplitudes in QCD, N=4 super Yang-Mills, and self-dual Yang-Mills, supported by explicit proofs up to six points and extending to gravity theories.

Contribution

It introduces a novel conjecture linking gluon amplitudes across different theories, with partial proofs and implications for self-dual gravity.

Findings

Explicit proof for six-point amplitudes

Conjectured relations for higher-point amplitudes

Extension to self-dual gravity and supergravity

Abstract

We conjecture a simple relationship between the one-loop maximally helicity violating gluon amplitudes of ordinary QCD (all helicities identical) and those of N=4 supersymmetric Yang-Mills (all but two helicities identical). Because the amplitudes in self-dual Yang Mills have been shown to be the same as the maximally helicity violating ones in QCD, this conjecture implies that they are also related to the maximally helicity violating ones of N=4 supersymmetric Yang-Mills. We have an explicit proof of the relation up to the six-point amplitude; for amplitudes with more external legs, it remains a conjecture. A similar conjecture relates amplitudes in self-dual gravity to maximally helicity violating N=8 supergravity amplitudes.