Prepared for submission to JHEP Scanning Tunneling Macroscopy, Black Holes and AdS/CFT Bulk Locality

Abstract: We establish resolution bounds on reconstructing a bulk field from bound-ary data on a timelike hypersurface. If the bulk only supports propagating modes, re-construction is complete. If the bulk also supports evanescent modes, local reconstruc-tion is not achievable unless one has exponential precision in knowledge of the boundary data. Without exponential precision, for a Minkowski bulk, one can reconstruct a spa-tially coarse-grained bulk field, but only out to a depth set by the coarse-graining scale. For an asymptotically AdS bulk, reconstruction is limited to a spatial coarse-graining proper distance set by the AdS scale. AdS black holes admit evanescent modes. We study the resolution bound in the large AdS black hole background and provide a dual CFT interpretation. Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators. Specifically, in order to probe the bulk on sub-AdS scales using only boundary data in terms of local operators, one must either have such data to exponential precision or make further assumptions about the bulk state. ar X i