Supertwistor space for 6D maximal super Yang-Mills

TL;DR

This paper develops a superspace formulation of 6D maximal super Yang-Mills using twistors, enabling new insights into amplitudes and off-shell structures, and confirming results with BCFW recursion.

Contribution

It introduces a non-chiral superspace for 6D super Yang-Mills using twistors, facilitating amplitude calculations and off-shell analysis, which was not previously available.

Findings

Derived 3,4,5-point tree amplitudes in 6D superspace.

Confirmed amplitudes using BCFW recursion.

Matched 6D results with off-shell 4D N=4 super Yang-Mills.

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.