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From what i understand string theory usually lives in a Minkowski Spacetime or AdS spacetime.

In Minkowski Spacetime conservation of energy is usually very straightforward, is this also the case in string theory?

For AdS space correct me if im wrong but Energy conservation can discussed in the context of AdS/CFT correspondence. Energy conservation in the CFT translates to certain constraints or conditions on the behavior of the gravitational fields in the bulk AdS spacetime. does this mean that energy is conserved in string theory or did i misunderstand something?

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