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.

arXiv comment28 pages, LaTeX, no figures

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Cited by in corpus (4)

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• HKLL for the Non-Normalizable Mode
• Extension of the HKLL bulk reconstruction for small $\Delta$
• CFT reconstruction of local bulk operators in half-Minkowski space