  Phenomenologically appealing supersymmetric grand unified theories have large
gauge representations and thus are not asymptotically free. Their ultraviolet
validity is limited by the appearance of a Landau pole well before the Planck
scale. One could hope that these theories save themselves, before the inclusion
of gravity, by generating an interacting ultraviolet fixed point, similar to
the one recently discovered in non-supersymmetric gauge-Yukawa theories.
Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of
other central charges we nonperturbatively rule out this possibility for a
broad class of prime candidates of phenomenologically relevant supersymmetric
grand unified theories. We also uncover candidates passing these tests, which
have either exotic matter or contain one field decoupled from the
superpotential. The latter class of theories contains a model with the minimal
matter content required by phenomenology.

High Energy Physics - Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology