  Among the broad spectrum of systems predicted to exhibit topological
superconductivity and Majorana fermions, one-dimensional wires with strong
spin-orbit coupling provide one of the most promising experimental candidates.
Here we investigate the fate of the topological superconducting phase in such
wires when repulsive interactions are present. Using a combination of Density
Matrix Renormalization Group, bosonization, and Hartree-Fock techniques, we
demonstrate that while interactions degrade the bulk gap -consistent with
recent results of Gangadharaiah et al.- they also greatly expand the parameter
range over which the topological phase arises. In particular, we show that with
interactions this phase can be accessed over a broader chemical potential
window, thereby leading to greater immunity against disorder-induced chemical
potential fluctuations in the wire. We also suggest that in certain wires
strong interactions may allow Majorana fermions to be generated without
requiring a magnetic field.
