  It has long been thought that macroscopic phase coherence breaks down in
effectively lower-dimensional superconducting systems even at zero temperature
due to enhanced topological quantum phase fluctuations. In quasi-1D wires,
these fluctuations are described in terms of "quantum phase-slip" (QPS):
tunneling of the superconducting order parameter for the wire between states
differing by $\pm2\pi$ in their relative phase between the wire's ends. Over
the last several decades, many deviations from conventional bulk
superconducting behavior have been observed in ultra-narrow superconducting
nanowires, some of which have been identified with QPS. While at least some of
the observations are consistent with existing theories for QPS, other
observations in many cases point to contradictory conclusions or cannot be
explained by these theories. Hence, a unified understanding of the nature of
QPS, and its relationship to the various observations has yet to be achieved.
In this paper we present a new model for QPS which takes as its starting point
an idea originally postulated by Mooij and Nazarov [Nature Physics {\bf 2}, 169
(2006)]: that \textit{flux-charge duality}, a classical symmetry of Maxwell's
equations, can be used to relate QPS to the well-known Josephson tunneling of
Cooper pairs. Our model provides an alternative, and qualitatively different,
conceptual basis for QPS and the phenomena which arise from it in experiments,
and it appears to permit for the first time a unified understanding of
observations across several different types of experiments and materials
systems.
