  We study the interplay between disorder and interaction in one-dimensional
topological superconductors which carry localized Majorana zero-energy states.
Using Abelian bosonization and the perturbative renormalization group (RG)
approach, we obtain the RG-flow and the associated scaling dimensions of the
parameters and identify the critical points of the low-energy theory. We
predict a quantum phase transition from a topological superconducting phase to
a non-topological localized phase, and obtain the phase boundary between these
two phases as a function of the electron-electron interaction and the disorder
strength in the nanowire. Based on an instanton analysis which incorporates the
effect of disorder, we also identify a large regime of stability of the
Majorana-carrying topological phase in the parameter space of the model.
