Conformally mapping HKLL to flat space
Abstract
We study two conformal images of the HKLL reconstruction problem for a conformally coupled scalar on AdS3. The first mapping is to a Dirichlet problem on one half of the Einstein static universe. A further conformal transformation maps this half-ESU problem to a massless scalar in a region of (2+1)-dimensional Minkowski space bounded by an uniformly accelerated circular Dirichlet mirror. However, the global HKLL problem, the resulting flat-space problem is not a generic local mirror problem with arbitrary boundary data. Rather, the mirror response data must belong to a restricted spectral class inherited from normalizable global AdS modes. We formulate and solve this restricted mirror problem intrinsically in flat space. In the process, we find an example of a valid smearing function which itself does not satisfy the equations of motion. We further consider AdS-Rindler wedge reconstruction. By conformal mapping to an appropriate coordinate system in flat space, we find a simple way to see the blow-up of the smearing function.
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BibTeX
@misc{kajuri2026conformally,
title = {{Conformally mapping HKLL to flat space}},
author = {Nirmalya Kajuri and Rhitaparna Pal},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.08593},
eprint = {2608.08593},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08593},
}
RIS
TY - UNPB
TI - Conformally mapping HKLL to flat space
AU - Nirmalya Kajuri
AU - Rhitaparna Pal
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.08593
UR - https://arxiv.org/abs/2608.08593
AB - We study two conformal images of the HKLL reconstruction problem for a conformally coupled scalar on AdS_3. The first mapping is to a Dirichlet problem on one half of the Einstein static universe. A further conformal transformation maps this half-ESU problem to a massless scalar in a region of (2+1)-dimensional Minkowski space bounded by an uniformly accelerated circular Dirichlet mirror. However, the global HKLL problem, the resulting flat-space problem is not a generic local mirror problem with arbitrary boundary data. Rather, the mirror response data must belong to a restricted spectral class inherited from normalizable global AdS modes. We formulate and solve this restricted mirror problem intrinsically in flat space. In the process, we find an example of a valid smearing function which itself does not satisfy the equations of motion. We further consider AdS-Rindler wedge reconstruction. By conformal mapping to an appropriate coordinate system in flat space, we find a simple way to see the blow-up of the smearing function.
ER -