Rigid D6-branes on T6 / ( Z₂ ×Z_2M ×WR ) {{{{T^6}}} left/ {{left( {{Z_2} times {Z_{2M}} times Omega mathcal{R}} right)}} right.} with discrete torsion

摘要

We give a complete classification of T6 / ( mathbbZ₂ ×mathbbZ_2M ×WR ) {{{{T^6}}} left/ {{left( {{mathbb{Z}_2} times {mathbb{Z}_{2M}} times Omega mathcal{R}} right)}} right.} 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 mathbbZ₂ ×mathbbZ₆ {mathbb{Z}_2} times {mathbb{Z}_6} and mathbbZ₂ ×mathbbZ₆¢ {mathbb{Z}_2} times mathbb{Z}_6^{prime} 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 mathbbZ₂ ×mathbbZ₄ {mathbb{Z}_2} times {mathbb{Z}_4} background is ruled out by simple arguments.