Supersymmetric quantum mechanics on a Kähler space
We prove that the classical part of the Nicolai map for a supersymmetric free nonrelativistic particle moving on a Kähler manifold is linear in the Kähler metric and local for its velocity. Moreover, we give an exact expression for the one-loop correction of the map in terms of the Kähler potential and point out a direct way to higher loop order. This provides another example for the rare cases of exact Nicolai maps, and the first all-order one-loop result. As a check we have verified the Nicolai-map conditions to zero and one-loop order (free-action and determinant-matching). A graphical representation is given as well.
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