Note on a NAHE Variation

We present a variation of the NAHE-basis for free fermionic heterotic string mod- els. By rotating some of boundary conditions of the NAHE periodic/anti-periodic fermions {ym, ym, wm, wm,}, for m = 1 to 6, associated with the six compact dimen- sions of a bosonic lattice/orbifold model, we show an additional method for enhancing the standard NAHE gauge group of SO(10) back to E6. This rotation transforms (SO(10) ⊗ SO(6)3)rmobs ⊗ (E8)hid into (E6 ⊗ U(1)5)obs ⊗ SO(22)hid. When SO(10) is enhanced to E6 in this manner, the ith MSSM matter generation in the SO(10) 16i rep, originating in twisted basis vector bi, recombines with both its associated untwisted MSSM Higgs in a 10i rep and an untwisted non-Abelian singlet φi, to form a 27i rep of E6. Beginning instead with the E6 model, the inverse transformation of the fermion boundary conditions corresponds to partial GUT breaking via boundary rotation. Correspondence between free fermionic models with Z2 ⊗Z2 twist (especially of the NAHE class) and orbifold models with a similar twist has received further attention recently. Our NAHE variation also involves a Z2 ⊗ Z2 twist and offers additional understanding regarding the free fermion/orbifold correspondence. Further, models based on this NAHE variation offer some different phenomenological features compared to NAHE-based models. In particular, the more compact Z2 ⊗ Z2 twist of the NAHE variation offers a range of mirror models not possible from NAHE-based models.