Nicolai maps on manifolds

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Abstract
In spite of the presence of quartic fermion interactions, we construct Nicolai maps for the empty and filled sectors of the N=2 supersymmetric σ model in 1+0 dimensions. The maps form covariant Langevin-Fokker-Planck systems on arbitrary manifolds without boundary and describe Brownian motion along geodesics. On compact manifolds, these stochastic systems always equilibrate to the probability densities of the empty and filled supersymmetric ground states.