  Recent experiments on short MoGe nanowires show a sharp
superconductor-insulator transition tuned by the normal state resistance of the
wire, with a critical resistance of $R_c\approx R_Q= h/(4e^2)$. These results
are at odds with a broad range of theoretical work on Josephson-like systems
that predicts a smooth transition, tuned by the value of the resistance that
shunts the junction. We develop a self-consistent renormalization group
treatment of interacting phase-slips and their dual counterparts, correlated
cooper pair tunneling, beyond the dilute approximation. This analysis leads to
a very sharp transition with a critical resistance of $R_Q$. The addition of
the quasi-particles' resistance at finite temperature leads to a quantitative
agreement with the experimental results. This self-consistent renormalization
group method should also be applicable to other physical systems that can be
mapped onto similar sine-Gordon models, in the previously inaccessible
intermediate-coupling regime.
