Quasilocal conserved charges and holography

We construct a quasilocal formalism for conserved charges in a theory of gravity in the presence of matter fields that may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion, and so it is irrespective of ambiguities in the total derivatives of the Lagrangian. By using identically conserved currents, we show that this formalism leads to the same expressions of conserved charges as those in the covariant phase space approach. At the boundary of the asymptotic anti-de Sitter space, we also introduce an identically conserved boundary current that has the same structure as the bulk current and then show that this boundary current gives us the holographic conserved charges identical with those from the boundary stress tensor method. In our quasilocal formalism, we present a general proof that conserved charges from the bulk potential are identical with those from the boundary current. Our results can be regarded as the extension of the existing results on the equivalence of conserved charges by the covariant phase space approach and by the boundary stress tensor method.