The possible gauge symmetries of gauged N=8 supergravity are discussed and an E7 basis is chosen in which the minimal couplings take a simple form. An SO(p,q) gauge symmetry (p+q=8) is spontaneously broken down to at least SO(p)*SO(q), while a theory with the gauge group CSO(p,q) is broken to SO(p)*U(1)q(-1)/2 but has a global SO(q) symmetry. The scalar potentials are examined for critical points at which the expectation value of the scalar field is SO(p)*SO(q) invariant. The SO(4,4) and SO(5,3) gaugings have non-supersymmetric SO(4)*SO(4) and SO(5)*SO(3) invariant solutions, respectively, with positive cosmological constant. The CSO(2,6) gauging has a non-supersymmetric zero cosmological constant solution in which the fermion mass scale can be chosen arbitrarily. The most general gauge group, CSO(p,q,r), preserves a metric with p positive eigenvalues, q negative eigenvalues and r zero eigenvalues (p+q+r=8).
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C.M. Hull (1985) studied this question.