We continue to explore the possibility that the graviton in two dimensions
is related to a quadratic differential that appears in the anomalous contri
bution of the gravitational effective action for chiral fermions. A higher
dimensional analog of this field might exist as well. We improve the defini
ng action for this diffeomorphism tensor field and establish a principle fo
r how it interacts with other fields and with point particles in any dimens
ion. All interactions are related to the action of the diffeomorphism group
. We discuss possible interpretations of this field.