BRST quantization of string question

simic4
Hi,

I am confused about the following, I was hoping someone could help:

The context: Polchinski Ch. 4.2, specifically equations 4.3.1a-c

I am verifying the BRST invariance of the bosonic string action (after one has integrated out B, and the weyl ghost),, I notice that one must use the ghost field equations of motion! d_bar c = 0 = d_bar b = 0.

i am not accustomed to being able to use equations of motion inside actions! why is this allowed..? Furthermore,, doesn't this make the whole process of deriving the brst current (eq 4.3.3) from Noether's theorem rather arbitrary?

This problem cannot be totally removed by checking BRST invariance from the "other" action (the action in 4.2.3,, the one before one integrates out B) because for the bosonic part to be invariant, one must assume c holomorphic,, ie d_bar c = 0.

perhaps i am missing a rather subtle point..

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