A New Class of Supersymmetric Orientifolds with D-Branes at Angles

TL;DR

This paper introduces a novel class of supersymmetric orientifolds, called $A3\cal R$ orientifolds, formed by combining world-sheet parity with a reflection on the internal tori, and analyzes how tadpole cancellation, gauge groups, and massless spectra depend on the complex structure of the compactification. The authors provide a detailed construction for Z$_3$ in six and four dimensions, including the Klein bottle, annulus, and Möbius-strip amplitudes, showing how branes at angles and intersection multiplicities shape the open-string sector and yield $SO(8)$ in 6D or $SO(4)$ in 4D, with anomaly cancellation ensured by both untwisted and twisted sectors. They further summarize results for Z$_4$, Z$_6$, and Z$_6'$ orbifolds, revealing a landscape of inequivalent models arising from different lattice orientations and brane configurations, including unitary gauge factors and discrete Wilson-line effects. Overall, this work expands the perturbative string vacua by introducing geometry-controlled SUSY-brane configurations, connecting to T-duality with B-field moduli and providing a framework to tune gauge content via internal geometry.

Abstract

We describe a new class of supersymmetric orientifolds which combine the world-sheet parity transformation with a complex conjugation in the compact directions. As an example, we investigate in detail the orientifold of the Z_3 toroidal orbifold in six and four dimensions. We demonstrate how the solution to the tadpole cancellation conditions, the resulting gauge groups and the massless spectra depend on the choice of the complex structures on the tori, giving rise to a variety of inequivalent models. We also summarize the results for the orientifolds of the Z_4, Z_6 and Z_6' orbifolds in four and six dimensions.