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Background independence
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===String theory=== [[String theory]] is usually formulated with [[perturbation theory]] around a fixed background. While it is possible that the theory defined this way is locally background-invariant, if so, it is not manifest, and it is not clear what the exact meaning is. One attempt to formulate string theory in a manifestly background-independent fashion is [[string field theory]], but little progress has been made in understanding it. Another approach is the conjectured, but yet unproven [[AdS/CFT correspondence|AdS/CFT duality]], which is believed to provide a full, non-perturbative definition of string theory in spacetimes with [[anti-de Sitter space|anti-de Sitter]] asymptotics. If so, this could describe a kind of [[superselection|superselection sector]] of the putative background-independent theory. But it would still be restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe. A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking. Topology change is an established process in [[string theory]].
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