Abstract
We discuss the extension of the HKLL (Hamilton, Kabat, Lifschytz, and Lowe) bulk reconstruction for non-interacting scalar fields corresponding to conformal weights ∆ smaller than the original condition ∆ > d − 1. We give explicit formulas for the cases d − 2 < ∆ ≤ d − 1 and ∆ = 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.
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Aoki, S., Balog, J. HKLL bulk reconstruction for small ∆. J. High Energ. Phys. 2022, 15 (2022). https://doi.org/10.1007/JHEP02(2022)015
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DOI: https://doi.org/10.1007/JHEP02(2022)015