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Is it possible to prove background independence of string theory? I've seen a few things about it but not really sure how it works. I seems to involve the action:

$$S = \int \sqrt{G}G^{\mu\nu}(X)\eta^{ab}\partial_a X_\mu(\sigma)\partial_b X_\nu(\sigma) d\sigma^2$$

And then expanding out the function $G^{\mu\nu}(X)$ so we get a non-polynomial action in $X^\mu(\sigma)$ to get a theory of string theory on curved space-time. But I can't see how this relates dynamical curved space time to the fields $X^\mu(\sigma)$.

  • I'm not sure what you're asking - the standard party line is that string theory formulated like that is not manifestly background-independent, so the answer to your question is "you can't". Why do you think you can prove background independence here? – ACuriousMind Jul 16 '18 at 20:34
  • But is General Relativity background independent? –  Jul 16 '18 at 20:35
  • That's an entirely different question. See e.g. https://physics.stackexchange.com/q/342025/50583. – ACuriousMind Jul 16 '18 at 20:43
  • Perturbative string theory is background-dependent. – Kosm Jul 16 '18 at 20:46
  • I don't think "is GR background independent?" is a meaningful question, because GR describes the dynamics of the background. – probably_someone Jul 16 '18 at 20:57
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    This particular action isn't background independent. However you might want to have a look at AdS-CFT correspondence, where you can precisely formulate questions about background independence in the context of asymptotically AdS spacetimes. – Bruce Lee Jul 16 '18 at 22:19

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