Possibility of optical unification in heterotic strings

Recently Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual minimal supersymmetric standard model unification below the string scale is extrapolated from the running of gauge couplings upward from $M_{Z^o}$ when an intermediate scale desert is assumed. In this paper we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the Nanopoulos-Antoniadis-Hagelin-Ellis (NAHE) set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within $\mathrm{SO}\left(10\right),$ giving the standard $k_Y=\frac{5}{3}$ hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic ${\mathrm{SU}\left(3\right)\mathrm{}}_C$ triplet-antitriplet pairs, ${\mathrm{SU}\left(2\right)\mathrm{}}_L$ doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is nonperturbatively chosen to cancel the FI D term $\xi$ generated by the anomalous $U\left(1\right)\mathrm{}$-breaking Green-Schwarz-Dine-Seiberg-Witten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway.