Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills

TL;DR

This paper proposes a generalized amplitude in planar N=4 super Yang-Mills that restores key superconformal symmetries and uses it to analyze two-loop MHV amplitudes, providing new insights into symmetry structures.

Contribution

It introduces a generalized amplitude depending on extra Grassmann variables that restores half of the superconformal symmetries and all dual superconformal symmetries in planar N=4 SYM.

Findings

The generalized amplitude restores significant superconformal symmetries.

The total differential of two-loop MHV amplitudes is obtained and verified.

Potential all-loop symmetry constraints are discussed.

Abstract

Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of scattering amplitudes which depends on twice as many Grassmann variables. We conjecture that it restores at least half of the superconformal symmetries, and all of the dual superconformal symmetries. The object arises naturally as the dual of a null polygonal Wilson loop in an $(x,\theta,\bar\theta)$ superspace. We support the conjecture by using it to obtain the total differential of all $n$-point two-loop MHV amplitudes, and showing that the result passes consistency checks. Potential all-loop constraints are also discussed.