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 ⊂ SO(1, 10) 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 ⊂ G where G are the generalized structure groups G = SO(d − 1, 1) × G(spacelike), G = ISO(d − 1) × G(null) and G = SO(d) × G(timelike) with 1 ≤ d < 11. For example, G(spacelike) = SO(16), G(null) = [SU(8) × U(1)] ⋉ R56 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. Research supported in part by DOE Grant DE-FG02-95ER40899. [email protected] [email protected]