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 η critical
exponent and it is shown that η is gauge independent, as expected on
physical grounds. In the scaling considered, η is found to be zero at
1-loop order, while ν≈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
η=ηXY​ should be contrasted with the negative values frequently
reported in the literature.Comment: EuroLaTex, 7 pages, 2 figures, reference updated; version to be
published in Europhysics Letter