Anomalous dimension of Dirac's gauge-invariant nonlocal order parameter in Ginzburg-Landau field theory

In a Ginzburg-Landau theory with n fields, the anomalous dimension of the gauge-invariant nonlocal order parameter defined by the long-distance limit of Dirac's gauge-invariant two-point function is calculated. The result is exact for all n to first order in ε≡4−d, and for all d∈(2,4) to first order in 1/n, and coincides with the previously calculated gauge-dependent exponent in the Landau gauge.