Critical fluctuations in superconductors and the magnetic field penetration depth

The superconducting transition is studied within the one-loop renormalization group in fixed dimension $D=3$ and at the critical point. A tricritical behavior is found, and for $\kappa > \kappa_c$, an attractive charged fixed point, distinct from that of a neutral superfluid. The critical exponents of the continuous transition are evaluated, and it is shown that the anomalous dimension of the gauge field equals unity. This implies the proportionality of the magnetic field penetration depth and the superconducting correlation length below the transition. The penetration depth exponent is nonclassical. We argue that it can not be extracted from the dual theory in a straightforward manner since it is not renormalized by fluctuations of the dual field.