On the construction of local fields in the bulk of AdS_5 and other spaces

TL;DR

Addresses how to reconstruct local bulk physics from boundary data in AdS5 and nonconformal Dp-brane geometries. Introduces a transfer function (Green's function) that maps boundary operators to bulk fields in the Poincaré patch and derives the appropriate mode functions for both conformal and nonconformal cases. Proves bulk locality in the conformal case via boundary commutators and Källén-Lehmann, and verifies locality in the D2-brane nonconformal setup, outlining the extension to interacting theories at order 1/N. Provides a concrete framework for analyzing bulk-boundary locality in holographic contexts and sets the stage for perturbative treatment of interactions.

Abstract

In the Poincare patch of Minkovski AdS_5 we explicitly construct local bulk fields from the boundary operators, to leading order in 1/N. We also construct the Green's function implicitly defined by this procedure. We generalize the construction of local fields for near horizon geometries of Dp branes. We try to expand the procedure to the interacting case, with partial success.