Hidden spacetime symmetries and generalized holonomy in M-theory

In M-theory vacua with vanishing 4-form F-(4), one can invoke the ordinary Riemannian holonomy H subset of SO(10, 1) to account for unbroken supersymmetries n = 1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid for non-zero F-(4), can account for more exotic fractions of supersymmetry, in particular 16 < n < 32. The conjectured holonomies are given by H subset of G, where G are the generalized structure groups G = SO(d - 1, 1) x G(spacelike), G = ISO(d - 1) x G(null) and G = SO(d) x G(timelike) with 1 less than or equal to d < 11. For example, G(spacelike) = SO(16), G(null) = [SU(8) x U(1)] x R-56 and G(timelike) = SO*(16) when d = 3. Although extending spacetime symmetries, there is no conflict with the Coleman-Mandula theorem. The holonomy conjecture rules out certain vacua which are otherwise permitted by the supersymmetry algebra. (C) 2003 Elsevier B.V. All rights reserved.