Chiral Squaring

TL;DR

The paper demonstrates that the states and symmetries of $\mathcal{N}=4$ SYM can be constructed by tensoring two $\mathcal{N}=1$ chiral multiplets and introducing two extra SUSY generators, enabling the maximal $\mathcal{N}=8$ supergravity to be written as four copies of the chiral multiplet. It extends this chiral-squaring framework to higher dimensions, deriving a gravity-chiral dictionary that connects gauge and gravity fields via a double-copy construction and clarifying the roles of non-abelian gauge symmetry and $SU(4)$ R-symmetry. In $D=4$ the dictionary is explicit, mapping SYM operators to bilinears of chiral states and producing the full on-shell $\mathcal{N}=4$ multiplet; in $D\neq4$ squaring is even more straightforward, with the $\mathcal{N}=(2,0)$ tensor multiplet and $\mathcal{N}=(2,2)$ supergravity arising from tensor products of chiral and tensor multiplets. The work suggests practical applications to scattering amplitudes, including quadruple-copy relations for gravitational amplitudes and potential off-shell extensions via the double-copy structure.

Abstract

We construct the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four copies of the chiral multiplet. We extend this to higher dimensions and discuss applications to scattering amplitudes.

Figures (1)

• Figure 1: Susy generators of the chiral multiplet