  The free (4,0) superconformal theory in 6 dimensions and its toroidal
dimensional reductions are studied. The reduction to four dimensions on a
2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the
linearised gravity sector, interchanging the linearised Einstein equations and
Bianchi identities and giving a self-duality between strong and weak coupling
regimes. The possibility of this extending to an interacting form of the theory
is discussed and implications for the non-geometric picture of gravity that
could emerge are considered.
