Superconducting Strings in E₆

We discuss the appearance of superconducting strings in E₆ grand unification, keeping track of the magnetic monopole flux that precedes the formation of the string flux tube. This flux matching ensures compatibility with the quantum tunneling of a monopole-antimonopole pair on a metastable string. We identify two realistic E₆ models with superconducting (metastable) strings that also carry zero modes of the right handed Majorana neutrinos and dark matter particles. Depending on the symmetry breaking scale associated with the strings, the latter could be a source of observable gravitational waves, intermediate scale dark matter, and the observed baryon asymmetry via leptogenesis. Topologically stable superconducting strings also appear if the E₆ symmetry breaking leaves unbroken the Z₂ subgroup of Z₄, the center of $SO(10)$. The zero modes of the SM fermions are the charge carriers in this case. Finally, the flux matching condition ensures that the Aharanov-Bohm phase change in going around the metastable strings is an integer multiple of $2 π$ for all fields. The fields in the spinorial representation of SO(10) acquire a phase change of exp(± iπ) if taken around the topologically stable Z₂ string.