Gauge dependence of the order parameter anomalous dimension in the Ginzburg-Laudau model and the critical fluctuations in superconductors

The critical fluctuations of superconductors are discussed in a fixed dimension scaling suited to describe the type-II regime. The gauge dependence of the anomalous dimension of the scalar field is established exactly from the Ward-Takahashi identities. Its fixed-point value gives the eta critical exponent and it is shown that eta is gauge independent, as expected on physical grounds. In the scaling considered, eta is found to be zero at 1-loop order, while nu approximate to 0.63. This result is just the 1-loop values for the XY model obtained in the fixed-dimension renormalization group approach. It is shown that this XY behavior holds at all orders. The result eta = eta(XY) should be contrasted with the negative values frequently reported in the literature.