Is there a background independent closed string field theory?

Question

Analogous to the background independent open string field theory by Witten. If there isn't, what are the main stumbling blocks preventing its construction?

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Answer 1

An original article is

• Ashoke Sen, Barton Zwiebach, Quantum Background Independence of Closed String Field Theory (arXiv:hep-th/9311009)

An old spr comment by Sabbir Rahman gives a survey of the history of some of these developments.

More references are here.

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Comments

As far as I understand, Sen and Zweibach consider "usual" closed string theory, which is not manifestly background independent, and prove that the theories on different backgrounds are equivalent. However, Witten's theory uses the space of backgrounds (BCFTs) as a classical history space which is a manifestly background independent framework. The problem is that he considers BCFTs with different boundary behavior but the same worldsheet-bulk behavior. Apparently this is sufficient for the same reason ordinary open string field theory contains closed strings.

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However, one would like to have a closed string analogue, that is, a theory whose classical history space is the space of all CFTs. This would be framework with completely manifest background independence.

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Sure, but you asked "is there background independent CSFT?". The closest to *manifest* background invariance in CSFT that I am aware of is Sen, Zwiebach "Background Independent Algebraic Structures in Closed String Field Theory" ([arXiv:hep-th/9408053](http://arxiv.org/abs/hep-th/9408053))

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