  Electric-magnetic duality or S-duality, extending the symmetry of Maxwell's
equations by including the symmetry between Noether electric charges and
topological magnetic monopoles, is one of the most fundamental concepts of
modern physics. In two-dimensional systems harboring Cooper pairs, S-duality
manifests in the emergence of superinsulation, a state dual to
superconductivity, which exhibits an infinite resistance at finite
temperatures. The mechanism behind this infinite resistance is the linear
charge confinement by a magnetic monopole plasma. This plasma constricts
electric field lines connecting the charge-anti-charge pairs into electric
strings, in analogy to quarks within hadrons. Yet the origin of the monopole
plasma remains an open question. Here we consider a two-dimensional Josephson
junction array (JJA) and reveal that the magnetic monopole plasma arises as
quantum instantons, thus establishing the underlying mechanism of
superinsulation as two-dimensional quantum tunneling events. We calculate the
string tension and the dimension of an electric pion determining the minimal
size of a system capable of hosting superinsulation. Our findings pave the way
for study of fundamental S-duality in desktop experiments on JJA and
superconducting films.
