Icosahedral Supersymmetry

Crystallography of Icosahedral Crystals

The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal can not in general be viewed as a space-filling ar...

More icosahedral fulleroids

Icosahedral coincidence rotations

The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices …S-factors† and present a complete list of the possible rotations with S < 50.

Supersymmetry Without Supersymmetry

We present four-dimensional M -theory vacua with N > 0 supersymmetry which, from the perspective of perturbative Type IIA string theory, have N = 0. Such vacua can appear when the compactifying 7-manifold is a U(1) fibration. The missing superpartners are Dirichlet 0-branes. Someone unable to detect Ramond-Ramond charge would thus conclude that these worlds have no unbroken supersymmetry. In pa...

Supersymmetry without Supersymmetry

We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is nonsupersymmetric at high scales, but flows toward a strongly-coupled superconformal fixed point at low energies; or, alternatively, if the visible sector is localized near the infrared brane ...