D=6, N= (2,0) and N= (4,0) theories

Using a convolutive field-theoretic product, it is shown here that the "square" of an Abelian D=6, N=(2,0) theory yields the free D=6, N=(4,0) theory constructed by Hull, together with its generalized (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×gauge" paradigm.