2006/03/02 by Pietro Fré, P. Fre', Mario Trigiante +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Compactification (mathematics) #Cosmology and Gravitation Theories #Gauged supergravity #Group (periodic table) #Holonomy #Lie group #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Orientifold #Physics #Pure mathematics #Quantum mechanics #String theory #Supergravity #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2006.06.006
published as Nucl.Phys. B751 (2006) 343-375 · 38 pages, tar file containing LaTeX source and youngtab.sty
arxiv created 2006/03/02 · openalex publication_date 2006/06/24 · arxiv updated 2010/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we prove the theorem that there exists no 7--dimensional Lie group manifold G of weak G2 holonomy. We actually prove a stronger statement, namely that there exists no 7--dimensional Lie group with negative definite Ricci tensor RicIJ. This result rules out (supersymmetric and non--supersymmetric) Freund--Rubin solutions of M--theory of the form AdS4× G and compactifications with non--trivial 4--form fluxes of Englert type on an internal group manifold G. A particular class of such backgrounds which, by our arguments are excluded as bulk supergravity compactifications corresponds to the so called compactifications on twisted--tori, for which G has structure constants τKIJ with vanishing trace τJIJ=0. On the other hand our result does not have bearing on warped compactifications of M--theory to four dimensions and/or to compactifications in the presence of localized sources (D--branes, orientifold planes and so forth). Henceforth our result singles out the latter compactifications as the preferred hunting grounds that need to be more systematically explored in relation with all compactification features involving twisted tori.