HKLL bulk reconstruction for small $\Delta$

Abstract

We discuss the extension of the HKLL (Hamilton, Kabat, Lifschytz, and Lowe) bulk reconstruction for non-interacting scalar fields corresponding to conformal weights $\Delta$ smaller than the original condition $\Delta >d-1$. We give explicit formulas for the cases $d-2<\Delta \le d-1$ and $\Delta =d-s$ with integer $s$. In the latter case we show that smearing CFT fields over a region of the boundary consisting of points light-like separated from the bulk point is sufficient for bulk reconstruction, whereas in general smearing over all light-like and space-like separated points is required.

28 pages, LaTeX, no figures

References in corpus (3)

• Holographic representation of local bulk operators
• CFT representation of interacting bulk gauge fields in AdS
• Holographic Representation of Higher Spin Gauge Fields