On the Role of Boundary Terms in the AdS/CFT Correspondence

TL;DR

This paper investigates the limitations of the standard AdS/CFT correspondence in capturing bulk information, proposing an extended prescription involving boundary terms and Noether currents to improve the mapping, especially for double-trace interactions.

Contribution

It introduces a generalized AdS/CFT prescription that incorporates boundary terms and Noether currents to better encode bulk information and handle double-trace interactions.

Findings

Standard AdS/CFT misses part of bulk information.

Extended prescription includes boundary terms and Noether currents.

Formalism effectively describes non-minimally coupled cases.

Abstract

We consider a scalar field theory on AdS, and show that the usual AdS/CFT prescription is unable to map to the boundary a part of the information arising from the quantization in the bulk. We propose a solution to this problem by defining the energy of the theory in the bulk through the Noether current corresponding to time displacements, and, in addition, by introducing a proper generalized AdS/CFT prescription. We also show how this extended formulation could be used to consistently describe double-trace interactions in the boundary. The formalism is illustrated by focusing on the non-minimally coupled case using Dirichlet boundary conditions.