In AdS/CFT, the story of renormalization has an elegant gravity dual. Regularizing the theory is done by putting a cutoff near the conformal boundary of AdS space, and renormalization is done by adding counterterms on that surface. Mathematically this is also interesting, since this utilizes the Lorentzian generalization of the Graham-Fefferman expansion.

But, in the spirit of “effective holography”, one ought to be able to do that in spacetimes which do not admit a conformal boundary. I am wondering if anyone has ever seen an attempt to systematically define holographic renormalization in such spaces, for example for p-branes ($p \neq 3$), the NS fivebrane, or the Sakai-Sugimoto model, etc. In such cases one can still take a cutoff surface at the UV of the theory, take the fields to be essentially non-fluctuating, but one does not have a conformal boundary and all the associated machinery.