Monopole catalysis of proton decay in SO(10) grand unified models

We construct the monopole spectrum in an SO(10) grand unified theory which has an arbitrary pattern of symmetry breakdown to SU(3)×U${\mathrm{}\left(1\right)\mathrm{}}_{\mathrm{EM}}$. We show that if the fermion fields are in a 16 of SO(10), then it is impossible to find an SO(10) theory where monopoles do not catalyze proton decay. Furthermore, the branching ratios for monopole-catalyzed proton decay are identical in SO(10) and SU(5) grand unified theories. We also present a criterion for constructing grand unified theories which do not have monopole catalysis of proton decay.