Supersymmetric Z_N times Z_M Orientifolds in 4D with D-Branes at Angles

TL;DR

This work constructs a class of Type IIA orientifolds on $T^6/({\mathbb Z}_N\times{\mathbb Z}_M)$ with $\Omega{\cal R}$, producing ${\cal N}=1$ in four dimensions and non-chiral spectra. By computing one-loop amplitudes (Klein bottle, annulus, Möbius strip) in the loop channel and enforcing RR tadpole cancellation, the authors determine D-6-brane configurations at angles and derive consistent gauge and matter content for several models, notably ${\mathbb Z}_4\times{\mathbb Z}_2$, ${\mathbb Z}_2\times{\mathbb Z}_2$, ${\mathbb Z}_6\times{\mathbb Z}_3$, and ${\mathbb Z}_3\times{\mathbb Z}_3$. The resulting massless spectra include an ${\cal N}=1$ supergravity multiplet plus non-chiral open-string sectors with gauge groups such as $[Sp(M/4)]^4$ and various bifundamentals; the work also discusses projective representations and dualities to Type IIB settings with discrete $B$-fields. Overall, the paper provides explicit globally consistent 4D orientifolds with rich D-brane sectors and sets the stage for further phenomenological exploration and connections to non-commutative field theories via dualities.

Abstract

We construct orientifolds of type IIA string theory. The theory is compactified on a T^6/Z_N times Z_M orbifold. In addition worldsheet parity in combination with a reflection of three compact directions is modded out. Tadpole cancellation requires to add D-6-branes at angles. The resulting four dimensional theories are N=1 supersymmetric and non-chiral.

Figures (7)

• Figure 1: a) Klein bottle, b) Möbius strip, c) Cylinder
• Figure 2: Lattices for ${\mathbb Z}_4 \times {\mathbb Z}_2$. Black circles denote the ${\mathbb Z}_4$ fixed points and white circles the additional ${\mathbb Z}_2$ fixed points.
• Figure 3: Arrangement of branes and action of the orbifold group for ${\mathbb Z}_4 \times {\mathbb Z}_2$. The branes are labelled by $(i_1,i_2) = (0,0), \ldots ,(3,1)$ mod $(4,2)$. This is convenient in the sense that the brane $(i_1,i_2)$ is obtained by rotating the compact real axes with $\Theta_1^{-i_1/2}\Theta_2^{-i_2/2}$, see also section \ref{['setup']}.
• Figure 4: Location of branes in the fundamental cells for ${\mathbb Z}_4 \times {\mathbb Z}_2$
• Figure 5: Arrangement of branes and action of the orbifold group for ${\mathbb Z}_2 \times {\mathbb Z}_2$. Inserting $n=0,1$ yields the four branes $(i_1,i_2) = (0,0), (1,0), (0,1), (1,1)$ mod $(2,2)$.