Static response of a N×N Josephson junction array

Duality and scaling techniques are applied to a N*N Josephson junction array to calculate the static Josephson current response at a junction ij, due to an applied transverse vector potential at kl. The long-wavelength response function vanishes suddenly above a Kosterlitz-Thouless transition temperature T KT , due to the onset of incoherence in the effective Josephson phase. The zero-frequency inverse kinetic inductance and the helicity modulus thus also drop at T KT , consistent with recent Monte Carlo calculations.