Intersecting D-Branes on Shift Z2 x Z2 Orientifolds

TL;DR

The paper analyzes shift Z2×Z2 orientifolds in Type IIA string theory, providing a complete classification of geometries and showing how type I, II, and III shifts modify both the orbifold topology (Hodge numbers) and the orientifold-plane content, thereby affecting RR tadpoles. It develops a homological framework to construct rigid and fractional D6-branes, including explicit exceptional cycles, and derives the spectrum, gauge groups, and consistency conditions (tadpoles, SUSY, K-theory, anomalies) for these backgrounds. The authors present a concrete (19,19) example yielding a fully rigid, two-generation Pati-Salam-like visible sector with no open-string moduli, illustrating the feasibility of semi-realistic model building in shift orientifolds. This work provides a systematic toolkit for exploring D-brane configurations on shift orientifolds and motivates future inclusion of fluxes and broader orbifold groups to approach realistic phenomenology.

Abstract

We investigate Z2 x Z2 orientifolds with group actions involving shifts. A complete classification of possible geometries is presented where also previous work by other authors is included in a unified framework from an intersecting D-brane perspective. In particular, we show that the additional shifts not only determine the topology of the orbifold but also independently the presence of orientifold planes. In the second part, we work out in detail a basis of homological three cycles on shift Z2 x Z2 orientifolds and construct all possible fractional D-branes including rigid ones. A Pati-Salam type model with no open-string moduli in the visible sector is presented.

Figures (5)

• Figure 1: Choices of complex structures, fixed points and fundamental cycles on one $\mathbb{T}^2$ factor.
• Figure 2: Hodge diamond for zero, one and two twisted sectors with fixed points.
• Figure 3: On the left one can see a brane which runs through two fixed points in each $\mathbb{T}^2$ factor and on the right the direct product of the brane in $\mathbb{T}^2_1\times\mathbb{T}^2_2$ is shown. The $\vartheta_{1,2}$ correspond to Wilson lines along the brane.
• Figure 4: Fractional branes for the case of Hodge numbers $(11,11)$. The type I shifts are $\delta=\frac{1}{2}(e_1^x+e_2^y)$ as indicated. The solid grey line is a fractional brane of type $\Pi_a^{F11}$ and its bulk-brane orbifold image is indicated as a dotted line. The black line is a fractional brane of type star ($\Pi_{\star\,b}^{F11}$) which is its own bulk-brane orbifold image.
• Figure 5: Example for the case of Hodge numbers $(19,19)$. The type I shift is $\delta=e_2^x+e_2^y$ as indicated. A fractional brane of type $\Pi_{\Theta}^{F19}$ is shown as a grey line and a fractional brane of type star ($\Pi_{\star\,b}^{F19}$) is drawn as a black line.