  We show that Majorana edge modes appear in a strongly correlated phase of
semiconducting nanowires with discrete rotational symmetry in the cross
section. These modes exist in the absence of spin-orbit coupling, magnetic
fields and superconductivity. They appear purely due to the combination of the
three-dimensional Coulomb interaction and orbital physics, which generates a
fermionic condensate exhibiting a topological ground state degeneracy in a
sector of the spectrum which is gapped to continuum modes. The gap can be
comparable in magnitude to the topological superconducting gap in other
solid-state candidate systems for Majorana edge modes, and may similarly be
probed via tunnel spectroscopy.
