Superstring NS tachyon vertex operator

Question

After reading some confusing chapter of various string theory book I'm trying to construct the Tachyon vertex operator for superstring theory. I know that this is removed after GSO projection, but for the moment I would like to construct this would-be vertex. It seems very strange to me that I couldn't find a systematic and precise treatment of this argument. However it seems to me rather natural (thought I didn't understand quite well why) to put an operator of the form

$$ e^{-\phi} $$

where $\phi$ is the field used to bosonize $\beta\gamma$ system. This operator has conformal weight $h=1/2$, so it must not be the end of the story. However this starting point is confirmed by Polchinski (vol. 2 eq (10.4.22)). Now what else shoud I add? I was thinking some momentum $$ e^{ikX(0,0)} $$ as it is done for the bosonic tachyon. But this operator has conformal weight $h=1$ itself and so I would get total conformal weight $h= 1 + 1/2 = 3/2$.

Then on the book by Blumenhagen et. al. I found this sentence:

"The ground state of NS sector is thus $e^{-\phi}c(0)|0\rangle.$" Which seems to me even wrong because the conformal weight of $c$ is $h=-1$

I know that I'm very confused about these superstring vertex operator. This is because I didn't find any book in which there is a comprehensible treatment. It would be of great help if someone provide a solution to this construction.

This post imported from StackExchange Physics at 2015-07-28 21:39 (UTC), posted by SE-user MaPo