Dual models of gauge unification in various dimensions

We construct a compactification of the heterotic string on an orbifold T6/Z6 leading to the standard model spectrum plus vector-like matter. The standard model gauge group is obtained as an intersection of three SO(10) subgroups of E8. Three families of SO(10)16-plets are localized at three equivalent fixed points. Gauge coupling unification favours existence of an intermediate GUT which can have any dimension between five and ten. Various GUT gauge groups occur. For example, in six dimensions one can have E6×SU(3), SU(4)×SU(4)×U(1)2 or SO(8)×SO(8), depending on which of the compact dimensions are large. The different higher-dimensional GUTs are 'dual' to each other. They represent different points in moduli space, with the same massless spectrum and ultraviolet completion.