Open string models with Scherk-Schwarz SUSY breaking and localized anomalies

Abstract

We study examples of chiral four-dimensional IIB orientifolds with Scherk--Schwarz supersymmetry breaking, based on freely acting orbifolds. We construct a new Z3xZ3' model, containing only D9-branes, and rederive from a more geometric perspective the known Z6'xZ2' model, containing D9, D5 and \bar D 5 branes. The cancellation of anomalies in these models is then studied locally in the internal space. These are found to cancel through an interesting generalization of the Green--Schwarz mechanism involving twisted Ramond--Ramond axions and 4-forms. The effect of the latter amounts to local counterterms from a low-energy effective field theory point of view. We also point out that the number of spontaneously broken U(1) gauge fields is in general greater than what expected from a four-dimensional analysis of anomalies.

Figures (3)

• Figure 1: The fixed-points structure in the ${\bf Z}_6^\prime \times {\bf Z}_2^\prime$ model. We label the 12 $\theta$ fixed points with $P_{1bc}$ and the 12 $\theta\beta$ fixed points with $P_{1bc^\prime}$, each index referring to a $T^2$, ordered as in the figure. Similarly, we denote with $P_{a\bullet c}$ the 9 $\theta^2$ fixed planes filling the second $T^2$, and respectively with $P_{a^\prime b\bullet }$ and $P_{a^\prime b^\prime \bullet}$ the 16 $\theta^3$ fixed and $\theta^3\beta$ fixed planes filling the third $T^2$. The 32 $D\mathit{5}$-branes and the 32 $\bar{D} \mathit{5}$-branes are located at point 1 in the first $T^2$, fill the third $T^2$, and sit at the points $1$ and $1^\prime$ respectively in the second $T^2$.
• Figure 2: Brane positions along the SS direction for the ${\bf Z}_6^\prime\times {\bf Z}_2^\prime$ model. The different supersymmetries left unbroken at the massless level in the $\mathit{55}$ and $\mathit{\bar{5}\!\bar{5}}$ sectors are also indicated.
• Figure 3: The fixed-point structure in the ${\bf Z}_3 \times {\bf Z}_3^\prime$ model. We label the 9 $\alpha$ fixed planes with $P_{ab\bullet}$, the 27 $\alpha\beta$ fixed points with $P_{a^\prime bc}$, the 27 $\alpha\beta^2$ fixed points with $P_{a^{\prime\prime} bc}$, and the 3 $\beta$ fixed planes with $P_{\bullet\bullet c}$.