Antilocalization in a 2D Electron Gas in a Random Magnetic Field

We construct a supersymmetric field theory for the problem of a two-dimensional electron gas in a random, static magnetic field. We find a new term in the free energy in addition to those present in the conventional unitary $\sigma$ model, whose presence relies on the long-range nature of the disorder correlations. Under a perturbative renormalization group analysis of the free energy, the new term contributes to the scaling function at one-loop order and leads to antilocalization.