Instead of conclusion
In my opinion, it is a drawback of the string theory that it is too geometric:
Theory being geometric indicates that the classical limit has somehow been already taken. I think that the quantum theory should use algebraic description, instead of geometric.
Here we attempt to interpret some constructions of the pure spinor formalism in terms of abstract algebra. We observe that at least some aspects of the formalism get simplified, notably the relation between integrated and unintegrated vertices. At this point, however, this is not entirely convincing, at least for the following reasons:
Our results are only valid for the simplest nondegenerate background, . The correct description should, of course, be background-independent.
We only studied SUGRA, we did not attempt to say anything about the massive states
We think that this circle of ideas should be further developed.