Graduate BRST operator Q in string theory and string field theory

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

S = ∫ Q_BΨ*Ψ + Ψ*Ψ*Ψ

There is a gauge invariance under δΨ = Q_BΛ. what is the framework in which the role of the BRST operator Q_B is understood in open string field theory?

 

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And how is this related to the worldsheet path integral with

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