Role of -ghost in classical SUGRA
We conclude that the -ghost, more precisely , is important in classical SUGRA:
it removes the nonphysical states
it explains the consistency of the SUGRA constraints at the nonlinear level
However, the -ghost is nonpolynomial. It would be fair to say that it is not sufficiently well understood.
an elementary argument for the consistency of the nonlinear theory might shed some light on the -ghost
(However, I do not know such argument)