Non-factorisable Bbb Z₂× Bbb Z₂heterotic orbifold models and Yukawa couplings

Abstract

We classify compactification lattices for supersymmetric Z 2 × Z 2 orbifolds. These lattices include factorisable as well as non-factorisable six-tori. Different models lead to different numbers of fixed points/tori. A lower bound on the number of fixed tori per twisted sector is given by four, whereas an upper bound consists of 16 fixed tori per twisted sector. Thus, these models have a variety of generation numbers. For example, in the standard embedding, the smallest number of net generations among these classes of models is equal to six, while the largest number is 48. Conditions for allowed Wilson lines and Yukawa couplings are derived.

Three generation magnetized orbifold models

“…Moreover, although we have concentrated on the factorizable torus, (T 2 ) 3 , it would be interesting to study possibilities for extensions to non-factorizable orbifolds [27]. …”

Classification of symmetric toroidal orbifolds

“…In the first one, the classification is based on Lie lattices [11], see also [31]. Again, this classification is somewhat incomplete: it misses four lattices and, in addition, neglects (38, 0)).…”

“…Therefore, model (1-1) in [10] corresponds to model A 4 of Förste et al [11], i.e. to the Lie lattice SU(4) × SU(2) 3 where the SU(4) part is an f-cubic lattice, see table 5.…”

“…Despite their simplicity, symmetric toroidal orbifolds provide us with a large number of different settings, which have, rather surprisingly, not been fully explored up to now. In the past, different attempts of classifying parts of these compactifications have been made [9][10][11][12]. As we shall see (in section 5.1.2) some of these classifications are mutually not consistent, and incomplete.…”

Orientifold's landscape: non-factorisable six-tori

“…However, it is very natural to ask whether more generic toroidal orientifold compactifications can be constructed. A first step in this direction has already been taken in heterotic theory [30][31][32][33][34][35], where orbifold models, which admit more complicated lattices, i.e. non factorisable lattices, were analysed.…”