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Consider a field theory coupled with gravity described by the action:

$S=\int d^Dx \sqrt{-g} \left( \mathcal{R}-\Lambda+\mathcal{L}_m[\phi] \right)$,

with the requirement that g must be asymptotically AdS.

Usually in AdS/CFT correspondence the action evaluated on-shell reduces to a purely boundary term.

Is there a general formula to express this boundary term?

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