Open questionsWe have seen that there is a zero mode, “asymmetric dilaton”, which is seen in the pure spinor formalism, but not present in SUGRA.Barring some mistake, there seem to be 2 possibilities:
This is a defect of the pure spinor formalism (or the form of it which we are using)
This is a defect of SUGRA, i.e. there are physical excitations which are not captured by SUGRA