Splitting Supersymmetry in String Theory

TL;DR

The paper proposes a string-theoretic realization of Split Supersymmetry using type I / magnetized D9-branes, achieving a spectrum with massless gauginos and higgsinos and superheavy scalars at leading order, while preserving gauge coupling unification. It demonstrates that unification can be maintained with appropriate geometric data and hypercharge embedding in a minimal three-stack setting, and it analyzes mechanisms—including discrete R-symmetry and a Dirac gravitino mass from KK towers—to keep gauginos light despite gravitational effects. A concrete three-stack SM embedding with sin^2\theta_W=3/8 at the GUT scale is presented, along with a discussion of gaugino/higgsino masses, SUSY-breaking scales, and the role of Scherk–Schwarz breaking. The phenomenology is confronted with gluino cosmology constraints, highlighting the cosmological viability of TeV-scale gluinos only for carefully chosen mass scales and cosmological histories. Overall, the work expands the landscape of string-inspired split SUSY models and suggests new channels for realistic model-building with a high string scale near $M_{\rm GUT}$.

Abstract

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^2θ_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^2θ_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.

Figures (1)

• Figure 1: Pictorial representation of models$A$, $B$ and $C$.