Continuum dual theory of the transition in 3D lattice superconductor

A recently proposed form of dual theory for three dimensional superconductor is rederived starting from the lattice electrodynamics and studied by renormalization group. The superfluid density below and close to the transition vanishes as an inverse of the correlation length for the disorder field. The corresponding universal amplitude is given by the fixed point value of the dual charge, and it is calculated to the leading order. The continuum dual theory predicts the divergence of the magnetic field penetration depth with the XY exponent, in contradiction to the results obtained from the Ginzburg-Landau theory for the superconducting order-parameter. Possible reasons for this difference are discussed.