DUALISATION OF DUALITIES

We analyse the global (rigid) symmetries that are realised on the boso nic fields of the various supergravity actions obtained from eleven-di mensional supergravity by toroidal compactification followed by the du alisation of some subset of fields. In particular, we show how the glo bal symmetries of the action can be affected by the choice of this sub set. This phenomenon occurs even with the global symmetries of the equ ations of motion. A striking regularity is exhibited by the series of theories obtained respectively without any dualisation, with the duali sation of only the Ramond-Ramond fields of the type IIA theory, with f ull dualisation to lowest degree forms, and finally for certain invers e dualisations (increasing the degrees of some forms) to give the type IIB series. These theories may be called the GL(A), D, E and GL(B) se ries, respectively. It turns out that the scalar Lagrangians of the E series are sigma models on the symmetric spaces K(E11-D)\E11-D (where K(G) is the maximal compact subgroup of G) and the other three series lead to models on homogeneous spaces K(G)\G times sign with bar connec ted to left of it R-s. These can be understood from the E series in te rms of the deletion of positive roots associated with the dualised sca lars, which implies a group contraction. We also propose a constrained Lagrangian version of the even-dimensional theories exhibiting the fu ll duality symmetry and begin a systematic analysis of abelian subalge bras. (C) 1998 Elsevier Science B.V.