Supersymmetry breaking, open strings and M-theory

TL;DR

This paper investigates supersymmetry breaking via the Scherk–Schwarz mechanism in type I string theory and its M-theory duals, showing that breaking in the bulk scales with the large radius while massless brane modes orthogonal to that dimension remain effectively supersymmetric. It develops two distinct open-string realizations: one with momentum-direction breaking that induces tree-level masses throughout, and another with branes orthogonal to the breaking direction where massless open-sector fields are protected and SUSY breaking is mediated mainly by gravity, yielding Planck-suppressed soft terms. The analysis spans nine- and six-dimensional setups, computing BPS spectra, one-loop vacuum energies, and scalar masses, and demonstrates intermediate-scale compactifications that are compatible with gauge coupling unification and a unification-scale string regime. The results highlight a non-perturbative (from the heterotic viewpoint) mechanism with potential phenomenological relevance, including dual descriptions in M-theory and Horava–Witten frameworks, and point toward extensions to chiral four-dimensional Type I models. Overall, the work clarifies how geometric compactification and brane orientation control the scale and mediation of SUSY breaking in open/closed string theories.

Abstract

We study supersymmetry breaking by Scherk-Schwarz compactifications in type I string theory. While in the gravitational sector all mass splittings are proportional to a (large) compactification radius, supersymmetry remains unbroken for the massless excitations of D-branes orthogonal to the large dimension. In this sector, supersymmetry breaking can then be mediated by gravitational interactions alone, that are expected to be suppressed by powers of the Planck mass. The mechanism is non perturbative from the heterotic viewpoint and requires a compactification radius at intermediate energies of order 10^{12}-10^{14} GeV. This can also explain the value of Newton's constant if the string scale is close to the unification scale, of order 10^{16} GeV.