Splitting Supersymmetry in String Theory
Résumé
We point out that type I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. We build such realistic U(3)xU(2)xU(1) models on stacks of magnetized D9-branes. Though not unified into a simple group, these theories preserve the successful supersymmetric relation of gauge couplings, as they start out with equal SU(3) and SU(2) couplings and the correct initial sin^2\\theta_W at the compactification scale of M_{GUT}\\simeq 2x10^{16} GeV, and they have the minimal low-energy particle content of split supersymmetry. We also propose a mechanism in which the gauginos and higgsinos are further protected by a discrete R-symmetry against gravitational corrections, as the gravitino gets an invariant Dirac mass by pairing with a member of a Kaluza-Klein tower of spin-3/2 particles. In addition to the models proposed here, split supersymmetry offers novel strategies for realistic model-building. So, TeV-scale string models previously dismissed because of rapid proton decay, or incorrect sin^2\\theta_W, or because there were no unused dimensions into which to dilute the strength of gravity, can now be reconsidered as candidates for realistic split theories with string scale near M_{GUT}, as long as the gauginos and higgsinos remain light.