Abstract

We construct the monopole spectrum in an SO(10) grand unified theory which has an arbitrary pattern of symmetry breakdown to SU(3)\ifmmode\times\else\texttimes\fi{}U${(1)}_{\mathrm{EM}}$. 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.

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