BRST operator Q in string theory and string field theory

In summary, the BRST operator Q is a fundamental mathematical operator that encodes the BRST symmetry in string theory and string field theory. It acts on string states by transforming them and plays a crucial role in maintaining the consistency and well-definedness of the theory. It is also intimately related to the Virasoro operator in string theory and can be extended to other theories beyond string theory and string field theory, such as gauge theories and topological field theories. This extension has led to significant advancements in our understanding of these theories.
  • #1
dx
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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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  • #2
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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