Nonuniversal gaugino masses from nonsinglet F-terms in nonminimal unified models

In phenomenological studies of low-energy supersymmetry, running gaugino masses are often taken to be equal near the scale of apparent gauge coupling unification. However, many known mechanisms can avoid this universality, even in models with unified gauge interactions. One example is an F-term vacuum expectation value that is a singlet under the standard model gauge group but transforms nontrivially in the symmetric product of two adjoint representations of a group that contains the standard model gauge group. Here, I compute the ratios of gaugino masses that follow from F-terms in nonsinglet representations of SO(10) and E-6 and their subgroups, extending well-known results for SU(5). The SO(10) results correct some long-standing errors in the literature.