Open Descendants of Z_2\times Z_2 Freely-Acting Orbifolds

TL;DR

This paper constructs and analyzes freely acting Z_2 x Z_2 shift orientifolds in Type I string theory, showing how momentum and winding shifts implement Scherk–Schwarz–like spontaneous SUSY breaking. It develops the open-descendant framework (Klein bottle, annulus, Möbius) to include D9 and D5 branes, and demonstrates that brane image multiplets arising from orbifold actions can reduce gauge ranks and generate rich, non-chiral spectra. It presents explicit models with N=2 → N=1 and N=4 → N=1 or N=2 breaking, discusses brane configurations, local tadpole cancellation, and M‑theory duals, and highlights how brane SUSY can persist on certain sectors while the bulk undergoes breaking. The results illustrate geometric mechanisms for partial SUSY breaking and provide a platform for exploring radiative corrections and effective field theories in non-chiral Horava–Witten–like setups.

Abstract

We discuss Z_2 \times Z_2 orientifolds where the orbifold twists are accompanied by shifts on momentum or winding lattice states. The models contain variable numbers of D5 branes, whose massless (and, at times, even massive) modes have variable numbers of supersymmetries. We display new type-I models with partial supersymmetry breaking N=2 \to N=1, N=4 \to N=1 and N=4 \to N=2. The geometry of these models is rather rich: the shift operations create brane multiplets related by orbifold transformations that support gauge groups of reduced rank. Some of the models are deformations of six-dimensional supersymmetric type-I models, while others have dual M-theory descriptions.