  Various ideas support the notion that the GUT gauge group might be a
semi-simple direct-product group such as $SU(5) \times SU(5)$. The
doublet-triplet splitting problem can be solved with a direct product group.
String theory suggests that the GUT scale is a modulus. Requiring this rules
out a single SU(5) gauge group. A model with $SU(5) \times SU(5)$ gauge
symmetry and the GUT scale as a modulus has been shown to exist. It is shown
that extending these ideas to $SO(10) \times SO(10)$ cannot be done with the
above requirement without unwanted massless modes at lower energy scales that
spoil the unification of couplings. Therefore these two conditions highly
constrain the class of possible GUT models.
