Self-Duality in Superconductor-Insulator Quantum Phase Transitions

It is argued that close to a Coulomb interacting quantum critical point, the interaction between two vortices in a disordered superconducting thin film separated by a distance $r$ changes from logarithmic in the mean-field region to $1\mathrm{/}r$ in the region dominated by quantum critical fluctuations. This gives support to the charge-vortex duality picture of the observed reflection symmetry in the current-voltage characteristics on both sides of the transition.