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Rigid D6-branes on \(T^{6}/({\mathbb Z}_{2} \times {\mathbb Z}_{2M} \times \Omega{\mathcal R})\) with discrete torsion. (English) Zbl 1214.81209
Summary: We give a complete classification of \(T^{6}/({\mathbb Z}_{2} \times {\mathbb Z}_{2M} \times \Omega{\mathcal R})\) orientifolds on factorisable tori and rigid D6-branes on them. The analysis includes the supersymmetry, RR tadpole cancellation and K-theory conditions and complete massless open and closed string spectrum (i.e. non-chiral as well as chiral) for fractional or rigid D6-branes for all inequivalent compactification lattices, without and with discrete torsion. We give examples for each orbifold background, which show that on \({\mathbb Z}_{2} \times {\mathbb Z}_{6}\) and \({\mathbb Z}_{2} \times {\mathbb Z}'_{6}\) there exist completely rigid D6-branes despite the self-intersections of orbifold image cycles. This opens up a new avenue for improved Standard Model building. On the other hand, we show that Standard and GUT model building on the \({\mathbb Z}_{2} \times {\mathbb Z}_{4}\) background is ruled out by simple arguments.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
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