N=8 GAUGINGS REVISITED - AN EXHAUSTIVE CLASSIFICATION

In this paper we reconsider, for N = 8 supergravity, the problem of ga uging the most general electric subgroup. We show that admissible theo ries are fully characterized by a single algebraic equation to be sati sfied by the embedding G(gauge) --> SL(8,R) subset of E-7(7) The compl ete set of solutions to this equation contains 36 parameters. Modding by the action of SL(8, R)) conjugations that yield equivalent theories all continuous parameters are eliminated except for an overall coupli ng constant and we obtain a discrete set of orbits. This set is in one -to-one correspondence with 36 Lie subalgebras of SL(8,R), correspondi ng to all possible real forms of the SO(8) Lie algebra plus a set of c ontractions thereof. By means of our analysis we establish the theorem that the N = 8 gaugings constructed by Hurl in the middle eighties co nstitute the exhaustive set of models. As a corollary we show that the re exists a unique seven-dimensional abelian gauging. The correspondin g abelian algebra is not contained in the maximal abelian ideal of the salvable Lie algebra generating the scalar manifold E-7(7)/SU(8) (C) 1998 Elsevier Science B.V.