Supertwistor space for 6D maximal super Yang-Mills

TL;DR

This work constructs a six-dimensional, non-chiral on-shell superspace for maximal SYM using 6D twistors, unifying MHV and non-MHV structures. It defines the on-shell supermomenta $q^{AI}=\lambda^{A}_{a}\eta^{aI}$ and $\tilde{q}_{AI'}=\tilde{\lambda}_{A\dot a}\tilde{\eta}^{\dot a}_{I'}$ and develops the full tree-level amplitudes for 4-, 3-, and 5-point processes via supersymmetrization of known 6D results, complemented by a BCFW analysis. The paper demonstrates explicit 4-point and 5-point SUSY amplitudes, derives the 3-point structure with SU(2) spinor variables, and shows compatibility with a BCFW program, while also reproducing the one-loop 4-point cut using superspace sums. This framework facilitates higher-dimensional unitarity techniques and provides a bridge to off-shell 4D $\mathcal{N}=4$ projective superspace, with potential impact on multi-loop D-dimensional SYM and gravity amplitudes.

Abstract

6D maximal super Yang-Mills on-shell amplitudes are formulated in superspace using 6 dimensional twistors. The 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction. In contrast to 4D this superspace is non-chiral, reflecting the fact that one cannot differentiate MHV from $\bar{\rm MHV}$ in 6D. Combined with unitarity methods, this superspace should be useful for the study of multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes. Furthermore, the non-chiral nature gives a natural framework for an off-shell construction. We show this by matching our result with off-shell D=4 N=4 super Yang-Mills amplitudes, expressed in projective superspace.

Figures (5)

• Figure 1: The weight space diagram for 4D N=4 super Yang-Mills
• Figure 2: The weight space diagram for 6D N=2 super Yang-Mills. Note that the gauginos are complex and there are two independent complex scalar field.
• Figure 3: The 4-point amplitude in the BCFW formalism. This is the only graph contributing if one chooses $1$ and $2$ as the shifted legs.
• Figure 4: The 5-point amplitude in the BCFW formalism. Now there are two graphs contributing if one chooses $1$ and $2$ as the shifted legs.
• Figure 5: Two-particle cut for one-loop 4-point amplitude.