Magnetized Four-Dimensional $Z_2 \times Z_2$ Orientifolds

TL;DR

This work investigates four-dimensional type I vacua derived from $Z_2 \times Z_2$ orbifolds and freely acting shift-orbifolds, incorporating uniform internal magnetic fluxes and a quantized NS-NS $B_{ab}$. The authors show that $B_{ab}$ is dual to asymmetric shifts and that magnetic deformations induce brane transmutation, enabling magnetized D9-branes to carry RR charges and mimic D5-branes, which can reduce gauge-group rank and produce multiple matter families. When D5-branes transverse to the magnetized directions are present, the low-energy spectrum can become chiral and anomaly-free under suitable tadpole conditions; self-dual flux configurations can avoid tachyons and even realize brane-supersymmetry breaking in some sectors. The results yield a rich set of magnetized 4D models with potential brane-intersection-induced chirality and avenues for brane-world phenomenology, while highlighting challenges in stability and moduli control that motivate further study of fluxes and geometric deformations.

Abstract

We study deformations of $Z_2 \times Z_2$ (shift-)orientifolds in four dimensions in the presence of both uniform Abelian internal magnetic fields and quantized NS-NS $B_{ab}$ backgrounds, that are shown to be equivalent to asymmetric shift-orbifold projections. These models are related by $T$-duality to orientifolds with $D$-branes intersecting at angles. As in corresponding six-dimensional examples, $D9$-branes magnetized along two internal directions acquire a charge with respect to the R-R six form, contributing to the tadpole of the orthogonal $D5$-branes (``brane transmutation''). The resulting models exhibit rank reduction of the gauge group and multiple matter families, due both to the quantized $B_{ab}$ and to the background magnetic fields. Moreover, the low-energy spectra are chiral and anomaly free if additional $D5$-branes longitudinal to the magnetized directions are present, and if there are no Ramond-Ramond tadpoles in the corresponding twisted sectors of the undeformed models.

Figures (1)

• Figure 1: $D5_1$ and $D5_2$ brane configurations for the $w_2 p_3$ model