Exact Holographic Kinematics in AdS/CFT
Abstract
We propose that holography contains an exact kinematic sector distinct from holographic dynamics. The appropriate setting for this sector is a CFT on an open solid torus in the Weyl frame. The open solid torus introduces an intrinsic scale, and the Weyl frame makes this scale manifest as an extra bulk direction. The resulting bulk-boundary pairs are exact and finite: no cutoff, large-N limit, strong-coupling assumption, or heavy-operator approximation is required. The AdS geometry appearing in this sector should be understood as a kinematic geometry; only in special CFTs and appropriate limits is it promoted to a dynamical semiclassical bulk. The standard boundary-anchored dictionary entries are recovered only as singular limits. As a striking demonstration, we show that Weyl-frame two-point functions provide a replica-free definition of entanglement entropy.
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BibTeX
@misc{yang2026exact,
title = {{Exact Holographic Kinematics in AdS/CFT}},
author = {Haitang Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.21252},
eprint = {2605.21252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21252},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Holographic Kinematics in AdS/CFT
AU - Haitang Yang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.21252
UR - https://arxiv.org/abs/2605.21252
AB - We propose that holography contains an exact kinematic sector distinct from holographic dynamics. The appropriate setting for this sector is a CFT on an open solid torus in the Weyl frame. The open solid torus introduces an intrinsic scale, and the Weyl frame makes this scale manifest as an extra bulk direction. The resulting bulk-boundary pairs are exact and finite: no cutoff, large-N limit, strong-coupling assumption, or heavy-operator approximation is required. The AdS geometry appearing in this sector should be understood as a kinematic geometry; only in special CFTs and appropriate limits is it promoted to a dynamical semiclassical bulk. The standard boundary-anchored dictionary entries are recovered only as singular limits. As a striking demonstration, we show that Weyl-frame two-point functions provide a replica-free definition of entanglement entropy.
ER -