Light-like retarded correlators and the horizon
Abstract
We show that retarded correlators in conformal field theories of scalar primary operators evaluated at finite temperature using AdS/CFT scale anomalously at large light like momenta. The anomalous scaling depends on the curvature of the horizon. Setting the momenta equal to the frequency ω, the retarded correlator for black holes with planar horizons scales as ω2/(d+2) (2Δ− d) as opposed to the scaling behaviour of ω2Δ− d expected by dimensional analysis at generic fixed momenta and large frequencies. Δ is the dimension of the primary and d, the number of space-time dimensions. For black holes with spherical and hyperbolic horizons when the frequency squared equals the Casimir along the horizon, the retarded correlator scales as ω(2Δ−d)/2 . We establish this using exact results in d=2, and a numerical analysis of the Heun equation for the AdS5 planar black hole and finally using the WKB approximation in general d. The exact result for black holes with hyperbolic horizon as well as the analysis at large d provides additional checks for the anomalous scaling behaviour. Finally we evaluate the anomalous scaling exponent for the stress tensor correlator in all its 3 channels.
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BibTeX
@misc{david2026lightlike,
title = {{Light-like retarded correlators and the horizon}},
author = {Justin R. David and Leonard Schwarze},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.24242},
eprint = {2607.24242},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24242},
}
RIS
TY - UNPB
TI - Light-like retarded correlators and the horizon
AU - Justin R. David
AU - Leonard Schwarze
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2607.24242
UR - https://arxiv.org/abs/2607.24242
AB - We show that retarded correlators in conformal field theories of scalar primary operators evaluated at finite temperature using AdS/CFT scale anomalously at large light like momenta. The anomalous scaling depends on the curvature of the horizon. Setting the momenta equal to the frequency ω, the retarded correlator for black holes with planar horizons scales as ω^2/(d+2) (2Δ− d) as opposed to the scaling behaviour of ω^2Δ− d expected by dimensional analysis at generic fixed momenta and large frequencies. Δ is the dimension of the primary and d, the number of space-time dimensions. For black holes with spherical and hyperbolic horizons when the frequency squared equals the Casimir along the horizon, the retarded correlator scales as ω^(2Δ−d)/2 . We establish this using exact results in d=2, and a numerical analysis of the Heun equation for the AdS_5 planar black hole and finally using the WKB approximation in general d. The exact result for black holes with hyperbolic horizon as well as the analysis at large d provides additional checks for the anomalous scaling behaviour. Finally we evaluate the anomalous scaling exponent for the stress tensor correlator in all its 3 channels.
ER -