Conclusions and open questions
The solution is parametrized by a constant vector —
the representation of the superconformal algebra induced from the representation of its bosonic part. It is necessary that satisfy some special conditions.
It must be true that some choices of lead to BRST-exact vertices (pure gauge), but the description of the subspace of such trivial ’s is an open problem.
On the other hand, it is demonstrated that at least for the finite-dimensional the choice leads to a nontrivial solution, corresponding to a dilaton/axion excitation.