HalfBPS M2brane orbifolds
Abstract
Smooth FreundRubin backgrounds of elevendimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7sphere by a freelyacting finite subgroup of SO(8). The classification is given in terms of ADE subgroups of the quaternions embedded in SO(8) as the graph of an automorphism. In this paper we extend this classification by dropping the requirement that the background be smooth, so that X is now allowed to be an orbifold of the round 7sphere. We find that if the background preserves more than half of the supersymmetry, then it is automatically smooth in accordance with the homogeneity conjecture, but that there are many halfBPS orbifolds, most of them new. The classification is now given in terms of pairs of ADE subgroups of quaternions fibred over the same finite group. We classify such subgroups and then describe the resulting orbifolds in terms of iterated quotients. In most cases the resulting orbifold can be described as a sequence of cyclic quotients.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 DOI:
 10.48550/arXiv.1007.4761
 arXiv:
 arXiv:1007.4761
 Bibcode:
 2010arXiv1007.4761D
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Group Theory
 EPrint:
 51 pages