  We develop a Gaussian variational approach in replica space to investigate
the phase diagram of a one-dimensional interacting disordered topological
superconducting wire in the strong coupling regime. This method allows for a
non-perturbative treatment in the disorder strength, electron- electron
interactions and the superconducting pairing amplitude. We find only two stable
phases: a topological superconducting phase, and a glassy, non-topological
localized phase, characterized by replica symmetry breaking.
