A“Periodic-Table”-for-SupersymmetricM-TheoryCompactifications.pdfVIP

CU-TP-1066 , HWS-200201 hep-th/0208030 A “Periodic Table” for Supersymmetric M-Theory Compactifications 1 1,2 Charles F. Doran and Michael Faux 1Departments of Mathematics and Physics Columbia University 2990 Broadway, New York, NY 10027 2 Department of Physics Hobart and William Smith Colleges Geneva, NY 14456 Abstract We develop a systematic method for classifying supersymmetric orbifold compactifi- cations of M-theory. By restricting our attention to abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a “periodic table” of such compactifications, organized according to the orbifolding group (order ≤ 12) and dimension (up to 7). An intriguing connection between supersymmetric orbifolds and G -structures is explored. 2 1 Introduction Manifolds with SU (N) holonomy have been a source of significant interest for mathe- maticians and physicists alike. Indeed, the importance of K3 manifolds and Calabi-Yau threefolds in the arena of consistent superstring background geometries could hardly be overstated. Aside from their undisputed beauty, compactification on these spaces allows for important control of supersymmetry which, in turn, permits ready access to poten- tially testable phenomenological consequences of string theory itself. It is for such reasons that understanding the geometry of these objects, including the classification of associated gauge bundles [1, 2, 3], has been such a relevant and fruitful end