(A)dS Holography with a Cut-off

TL;DR

This paper derives smearing functions relating bulk operators to boundary data at a cut-off surface in AdS, compares with de Sitter space, and discusses implications for holographic RG and bulk locality.

Contribution

It provides explicit smearing functions for a cut-off AdS surface and explores their relation to de Sitter space and holographic RG, advancing understanding of bulk-boundary correspondence.

Findings

Derived explicit smearing functions at a cut-off surface in AdS.

Compared AdS results with de Sitter space counterparts.

Discussed implications for holographic RG and bulk locality.

Abstract

We find out the smearing/ transfer functions that relate a local bulk operator with its boundary values at a cut-off surface located at $z=z_0$ of the AdS Poincar\'{e} patch. We compare these results with de Sitter counterparts and comment on their connections with corresponding construction for dS/ CFT. As the boundary values can help define the required field theory at $z=z_0$ and encode bulk locality in terms of it, our work can provide key information about holographic RG in the context of AdS/ CFT.