Hidden spacetime symmetries and generalized holonomy in M-theory ☆

Abstract In M-theory vacua with vanishing 4-form F (4) , one can invoke the ordinary Riemannian holonomy H ⊂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 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 G (spacelike)=SO(16), G (null) =[ SU (8)× U (1)]⋉ 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.