Matching Renormalisation Schemes in Holography

TL;DR

This paper investigates how to match regularisation and renormalisation schemes between bulk and boundary theories in holography, demonstrating scheme matching for Casimir energy in AdS/CFT and discussing implications for the RG interpretation.

Contribution

It provides a detailed analysis of scheme matching in holography, specifically showing how to align regularisation schemes for physical quantities like Casimir energy in AdS/CFT.

Findings

Scheme matching reproduces bulk AdS results with finite cutoff corrections

Regularisation choices can be aligned between bulk and boundary theories

Implications support the RG interpretation of holography

Abstract

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.