Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime
Abstract
We show that for bulk discrete series fields whose dual operators have integer conformal dimensions, the Generalised Energy Conservation (GEC) condition for de Sitter (dS) scattering amplitudes defined in even-dimensional extended Poincaré spacetime corresponds precisely to the absence of boundary conformal anomalies, including beta-function contributions, at the level of tree-level contact interactions. In contrast, holographic consistency in AdS/CFT enforces only the locality of the conformal anomaly. We find novel, unique four-point interactions involving three identical conformally coupled scalars and one discrete series scalar by performing both GEC and holographic bootstraps. This demonstrates that the solutions to GEC form a measure-zero subset of the holographically consistent solutions. Our holographic analysis agrees precisely with the expected renormalisation conditions for conformal field theory correlators. In addition, the constraint for a particular four-point configuration may be relevant for testing holographic consistency of scale-separated non-supersymmetric AdS4 vacua.
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BibTeX
@misc{du2026conformal,
title = {{Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime}},
author = {Zong-Zhe Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08113},
eprint = {2610.08113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08113},
note = {CC0},
}
RIS
TY - UNPB
TI - Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime
AU - Zong-Zhe Du
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.08113
UR - https://arxiv.org/abs/2610.08113
AB - We show that for bulk discrete series fields whose dual operators have integer conformal dimensions, the Generalised Energy Conservation (GEC) condition for de Sitter (dS) scattering amplitudes defined in even-dimensional extended Poincaré spacetime corresponds precisely to the absence of boundary conformal anomalies, including beta-function contributions, at the level of tree-level contact interactions. In contrast, holographic consistency in AdS/CFT enforces only the locality of the conformal anomaly. We find novel, unique four-point interactions involving three identical conformally coupled scalars and one discrete series scalar by performing both GEC and holographic bootstraps. This demonstrates that the solutions to GEC form a measure-zero subset of the holographically consistent solutions. Our holographic analysis agrees precisely with the expected renormalisation conditions for conformal field theory correlators. In addition, the constraint for a particular four-point configuration may be relevant for testing holographic consistency of scale-separated non-supersymmetric AdS_4 vacua.
ER -