Tripletless unification in the conformal window

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.