  A product SU(5)xSp(4) grand unified model is proposed with no fundamental
Higgs fields transforming under SU(5). Higgs doublets are instead embedded into
a four dimensional representation of the Sp(4) gauge group, and hence there is
no doublet-triplet splitting problem because there are no triplets. The Sp(4)
group contains enough matter to lie in the conformal window, causing its gauge
coupling to flow to a strongly-coupled infrared fixed-point at low energy,
naturally preserving gauge coupling unification to percent level accuracy.
Yukawa couplings, including the top, arise through dimension five operators
that are enhanced by the large anomalous dimension of the Higgs fields. Proton
decay mediated by dimension five operators is absent at the perturbative level.
It reappears, however, non-perturbatively due to Sp(4) instantons but the rate
is suppressed by a high power of the ratio of the dynamical scale to the
unification scale. With gravity- or gaugino-mediated supersymmetry breaking,
non-universal gaugino masses are predicted, satisfying specific one-loop
renormalization group invariant relations. These predictions should be easily
testable with the LHC and a linear collider.
