Abstract
We study the relation between a heterotic \({T^6 \left/ {{{{\mathbb{Z}}_6}}} \right.}\) orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a \({{\mathbb{Z}}_2}\) quotient of \({T^4 \left/ {{{{\mathbb{Z}}_3}}} \right.}\times {T^2}\). We consider a two-step resolution, whose intermediate step is \(\left( {K3\times {T^2}} \right){{\mathbb{Z}}_2}\). This allows us to identify the massless twisted states which correspond to the geometric Kähler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after higgsing does not even include the standard model gauge group. Moreover, after higgsing, the massless spectrum is non-chiral under the surviving gauge group.