$D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories

Using a convolutive field theoretic product, it is shown here that the “square” of an Abelian $D=6$, $\mathcal{N}=(2,0)$ theory yields the free $D=6$, $\mathcal{N}=(4,0)$ theory constructed by Hull, together with its generalised (super)gauge transformations. This offers a new perspective on the $(4,0)$ theory and chiral theories of conformal gravity more generally, while at the same time extending the domain of the “gravity = gauge $\times$ gauge” paradigm.