2003/03/31 by M. J. Duff, James T. Liu · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1016/j.nuclphysb.2003.09.019
published as Nucl.Phys. B674 (2003) 217-230 · Notes added addressing Hull's results in hep-th/0305039. We agree with the necessity of SL(32,R) for classifying generalized holonomy. References added. 18 pages, latex
arxiv created 2003/06/03 · openalex publication_date 2003/10/15 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In M-theory vacua with vanishing 4-form F, 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, 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) x G(spacelike), G=ISO(d-1) x G(null) and G=SO(d) x G(timelike) with 1<=d<11. For example, G(spacelike)=SO(16), G(null)=[SU(8) x U(1)] \ltimes 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.