Ghost number 2

The NSNS 3-form field strength should correspond to:


It turns out that the linearized SUGRA equations of motion are not satisfied, because . However, the derivatives of are all zero:


therefore this is a “zero mode effect”.

This is a puzzle. Most likely, the zero modes are not correctly reproduced in the current version of the pure spinor formalism. The disagreement in the zero mode sector was discussed in arxiv:1005.0049 and arxiv:1203.0677. It would be useful to explicitly trace the connection between the nonzero and the “non-physical” vertex found in those papers.