Magnetized Four-Dimensional $Z_2 \times Z_2$ Orientifolds

TL;DR

This paper explores deformations of four-dimensional $Z_2 imes Z_2$ orientifolds with magnetic fields and $B$-fields, revealing models with reduced gauge ranks, multiple matter families, and chiral, anomaly-free spectra through brane transmutation and background effects.

Contribution

It introduces novel deformations of $Z_2 imes Z_2$ orientifolds incorporating magnetic and $B$-field backgrounds, linking them to intersecting brane models and analyzing their low-energy spectra.

Findings

Models exhibit gauge rank reduction and multiple matter families.

Low-energy spectra are chiral and anomaly free with additional D5-branes.

Magnetic fields induce brane transmutation affecting tadpole cancellation.

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.