Oddness from Rigidness

TL;DR

This paper explores the construction of type IIA orientifolds on non-factorisable T^6/(Z2 x Z2) lattices with rigid D6-branes, demonstrating the feasibility of models with an odd number of families.

Contribution

It develops model building rules and consistency conditions for non-factorisable lattices with rigid D6-branes, enabling the construction of realistic models with odd families.

Findings

Odd number of families achievable in non-factorisable lattices.

Odd families also possible in factorisable cases without tilted tori.

Presented three-family Pati-Salam models with no chiral exotics.

Abstract

We revisit the problem of constructing type IIA orientifolds on T^6/(Z2 x Z2) which admit (non)-factorisable lattices. More concretely, we consider a (Z2 x Z2') orientifold with torsion, where D6-branes wrap rigid 3-cycles. We derive the model building rules and consistency conditions in the case where the compactification lattice is non-factorisable. We show that in this class of configurations, (semi) realistic models with an odd number of families can be easily constructed, in contrast to compactifications where the D6-branes wrap non-rigid cycles. We also show that an odd number of families can be obtained in the factorisable case, without the need of tilted tori. We illustrate the discussion by presenting three family Pati-Salam models with no chiral exotics in both factorisable and non-factorisable toroidal compactifications.