Tripletless unification in the conformal window

A product SU(5)xSp(4) grand unified model is proposed with no fundamentalHiggs fields transforming under SU(5). Higgs doublets are instead embedded intoa four dimensional representation of the Sp(4) gauge group, and hence there isno doublet-triplet splitting problem because there are no triplets. The Sp(4)group contains enough matter to lie in the conformal window, causing its gaugecoupling 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 operatorsthat are enhanced by the large anomalous dimension of the Higgs fields. Protondecay mediated by dimension five operators is absent at the perturbative level.It reappears, however, non-perturbatively due to Sp(4) instantons but the rateis suppressed by a high power of the ratio of the dynamical scale to theunification scale. With gravity- or gaugino-mediated supersymmetry breaking,non-universal gaugino masses are predicted, satisfying specific one-looprenormalization group invariant relations. These predictions should be easilytestable with the LHC and a linear collider.Comment: 15 pages, 1 figur