  In holography there is a one-to-one correspondence between physical
observables in the bulk and boundary theories. To define physical observables,
however, regularisation needs to be implemented in both sides of the
correspondence. It is arguable whether the correspondence should extend to
regularisation and renormalisation scheme which are not physical in the
conventional sense. However, if we are to take the renormalisation group (RG)
interpretation of holography seriously, its precise understanding appears to
require the matching of regularisations and renormalisation schemes in the bulk
and boundary theories. We address this question in the AdS_5/CFT_4
correspondence by considering a simplest physical quantity, the Casimir energy
of the N=4 super Yang-Mills (SYM) theory on R x S^3, in a {\zeta}-function
regularisation and show that there are choices of scheme which match the bulk
AdS result including the radial cutoff dependent corrections when the cutoff is
kept finite. We further discuss the implication of this result to the RG
interpretation of holography.
