181 research outputs found
Half-BPS M2-brane orbifolds
Smooth Freund-Rubin backgrounds of eleven-dimensional 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 7-sphere by
a freely-acting 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 7-sphere. 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 half-BPS 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.Comment: 51 pages; v3: substantial revision (20% longer): we had missed some
cases, but the paper now includes a check of our results via comparison with
extant classification of finite subgroups of SO(4
Hereditary Polytopes
Every regular polytope has the remarkable property that it inherits all
symmetries of each of its facets. This property distinguishes a natural class
of polytopes which are called hereditary. Regular polytopes are by definition
hereditary, but the other polytopes in this class are interesting, have
possible applications in modeling of structures, and have not been previously
investigated. This paper establishes the basic theory of hereditary polytopes,
focussing on the analysis and construction of hereditary polytopes with highly
symmetric faces.Comment: Discrete Geometry and Applications (eds. R.Connelly and A.Ivic
Weiss), Fields Institute Communications, (23 pp, to appear
D-branes on Singularities: New Quivers from Old
In this paper we present simplifying techniques which allow one to compute
the quiver diagrams for various D-branes at (non-Abelian) orbifold
singularities with and without discrete torsion. The main idea behind the
construction is to take the orbifold of an orbifold. Many interesting discrete
groups fit into an exact sequence . As such, the orbifold
is easier to compute as and we present graphical rules which
allow fast computation given the quiver.Comment: 25 pages, 13 figures, LaTe
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