Gauge dependenceof the order parameter anomalous dimension in the Ginzburg-Landau 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 stablished 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 $\nu\approx 0.63$. 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.