A new diagrammatic perturbative construction of Nicolai maps in Poincaré supergravity finds that the gravitino is required for consistency in the graviton sector at order κ², so Einstein gravity admits such a map only via its N=1 supersymmetric completion.
Is the Nicolai map unique?
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Perturbative Nicolai-Map Diagrammatics: Application to Poincar\'{e} Supergravity
A new diagrammatic perturbative construction of Nicolai maps in Poincaré supergravity finds that the gravitino is required for consistency in the graviton sector at order κ², so Einstein gravity admits such a map only via its N=1 supersymmetric completion.