  We investigate the effect of interacting quantum phase slips on persistent
current and its fluctuations in ultrathin superconducting nanowires and
nanorings pierced by the external magnetic flux. We derive the effective action
for these systems and map the original problem onto an effective sine-Gordon
theory on torus. We evaluate both the flux dependent persistent current and the
critical radius of the ring beyond which this current gets exponentially
suppressed by quantum fluctuations. We also analyze fluctuations of persistent
current caused by quantum phase slips. At low temperatures the supercurrent
noise spectrum has the form of coherent peaks which can be tuned by the
magnetic flux. Experimental observation of these peaks can directly demonstrate
the existence of plasma modes in superconducting nanorings.
