HKLL bulk reconstruction for small Δ

We discuss the extension of the HKLL (Hamilton, Kabat, Lifschytz, and Lowe) bulk reconstruction for non-interacting scalar fields corresponding to conformal weights increment smaller than the original condition Delta > d - 1. We give explicit formulas for the cases d - 2 < Delta <= 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.

Automated summary

We discuss the extension of the HKLL bulk reconstruction for non-interacting scalar fields with conformal weights increment smaller than the original condition. We provide explicit formulas for different cases and analyze the smearing requirements.