  A strong coupling limit of theories whose low-energy effective field theory
is 5-dimensional N=8 supergravity is proposed in which the gravitational
coupling becomes large. It is argued that, if this limit exists, it should be a
6-dimensional theory with (4,0) supersymmetry compactified on a circle whose
radius gives the 5-dimensional Planck length. The sector corresponding to the
D=5 supergravity multiplet is a (4,0) D=6 superconformal field theory based on
the (4,0) multiplet with 27 self-dual 2-forms, 42 scalars and, instead of a
graviton, a fourth-rank tensor gauge field satisfying a self-duality
constraint. The superconformal field theory has 32 supersymmetries and 32
conformal supersymmetries and its dimensional reduction gives the maximal
supergravity in five dimensions. Electromagnetic duality generalises to a
gravitational triality.
