A BRST operator Q in string theory and string field theory

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In string theory, physical states satisfy QBΨ = 0, where QB is the BRST operator. This equation of motion can be obtained from an action

S = ∫ QBΨ*Ψ + Ψ*Ψ*Ψ

There is a gauge invariance under δΨ = QBΛ. what is the framework in which the role of the BRST operator QB is understood in open string field theory?
 
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And how is this related to the worldsheet path integral with

$$S = \frac{1}{2\pi \alpha'} \int d^2z \ \partial X \bar{\partial}X$$
 
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