Magnetic Fluxes, NS-NS $B$ Field and Shifts in Four-Dimensional Orientifolds

TL;DR

The paper analyzes how freely acting orbifold actions, discrete deformations via the NS-NS $B_{ab}$ field, and internal uniform magnetic fluxes combine in four-dimensional orientifolds. It elucidates how quantized $B_{ab}$ values and shift-orbifolds relate to rank reductions in Chan-Paton groups, non-commuting Wilson lines, and brane multiplicities, and how magnetized branes can yield chiral spectra through Landau-level degeneracy and brane transmutations. By examining $Z_2 \times Z_2$ shift-orientifolds and magnetized orientifolds (notably the $w_1 w_2 p_3$ model), the work demonstrates mechanisms for achieving 4D chirality, controlled supersymmetry breaking, and consistent tadpole cancellation, contributing to the construction of semi-realistic string vacua. The findings highlight the interconnected roles of shifts, B-field backgrounds, and magnetic flux in shaping gauge groups, matter content, and anomaly cancellation in orientifold compactifications, with implications for string model building and phenomenology.

Abstract

We discuss the interplay between freely acting orbifold actions, discrete deformations and internal uniform magnetic fields in four-dimensional orientifold models.

Figures (3)

• Figure 1: $O_0$-planes configuration on a two-torus: a) $B=0$. b) $B \ne 0$
• Figure 2: $D_1$-brane configuration of the $\Omega \ R$ orientifold: a) $B=0$. b) $B \ne 0$
• Figure 3: $B$-field vs shift-orientifold: a) space filling $D_2$-branes with $B=0$. b) Doublets of $D_1$-branes in the shift-orientifold.