Dualisation of dualities II:: twisted self-duality of doubled fields and superdualities

We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hedge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted self-duality condition on the total field strength G, which takes its values in a Lie superalgebra. This doubling is invariant under dualisations; it allows a unification of the gauge symmetries of all degrees, including the usual U-dualities that have degree zero. These "superdualities" encompass the dualities for all choices of polarisation (i.e. the choices between fields and their duals). All gauge symmetries appear as subgroups of finite-dimensional supergroups, with Grassmann coefficients in the differential algebra of the spacetime manifold. (C) 1998 Published by Elsevier Science B.V.