  Topological superconductors represent one of the key hosts of Majorana-based
topological quantum computing. Typical scenarios for one-dimensional
topological superconductivity assume a broken gauge symmetry associated to a
superconducting state. However, no interacting one-dimensional many-body system
is known to spontaneously break gauge symmetries. Here, we show that zero modes
emerge in a many-body system without gauge symmetry breaking and in the absence
of superconducting order. In particular, we demonstrate that Majorana zero
modes of the symmetry-broken superconducting state are continuously connected
to these zero-mode excitations, demonstrating that zero-bias anomalies may
emerge in the absence of gauge symmetry breaking. We demonstrate that these
many-body zero modes share the robustness features of the Majorana zero modes
of symmetry-broken topological superconductors. We introduce a bosonization
formalism to analyze these excitations and show that a ground state analogous
to a topological superconducting state can be analytically found in a certain
limit. Our results demonstrate that robust Majorana-like zero modes may appear
in a many-body systems without gauge symmetry breaking, thus introducing a
family of protected excitations with no single-particle analogs.
