Carroll-Weyl symmetries in flat holography
Abstract
The degenerate geometry of a null boundary admits an enlarged local conformal freedom: in two dimensions, a Carrollian coframe allows two independent Weyl rescalings, one modulating and the other preserving the boundary volume form. We investigate whether both transformations can be realized as charged asymptotic symmetries in three-dimensional flat holography. We show that Einstein gravity canonically realizes the volume-modulating Carroll-Weyl transformation, together with local Carroll boosts, but does not admit the volume-preserving rescaling as an additional independent asymptotic symmetry. We trace this obstruction both back to the conformal completion of null infinity and to the absence of two independent commuting semisimple generators in the Poincaré algebra. Conformal gravity overcomes this obstruction through bulk dilatations, which supply the missing algebraic direction. We construct an asymptotically flat phase space of conformal gravity in which both types of Carroll-Weyl transformations and local Carroll boosts admit finite, integrable, and generically nonvanishing canonical charges, and derive their centrally extended algebra. Finally, we show that these central extensions arise from boundary anomalies through symplectic descent, yielding a gravitational prediction for Carroll-Weyl anomalies in flat holography.
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BibTeX
@misc{delfante2026carrollweyl,
title = {{Carroll-Weyl symmetries in flat holography}},
author = {Arnaud Delfante and Chrysoula Markou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36026},
eprint = {2609.36026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36026},
}
RIS
TY - UNPB
TI - Carroll-Weyl symmetries in flat holography
AU - Arnaud Delfante
AU - Chrysoula Markou
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36026
UR - https://arxiv.org/abs/2609.36026
AB - The degenerate geometry of a null boundary admits an enlarged local conformal freedom: in two dimensions, a Carrollian coframe allows two independent Weyl rescalings, one modulating and the other preserving the boundary volume form. We investigate whether both transformations can be realized as charged asymptotic symmetries in three-dimensional flat holography. We show that Einstein gravity canonically realizes the volume-modulating Carroll-Weyl transformation, together with local Carroll boosts, but does not admit the volume-preserving rescaling as an additional independent asymptotic symmetry. We trace this obstruction both back to the conformal completion of null infinity and to the absence of two independent commuting semisimple generators in the Poincaré algebra. Conformal gravity overcomes this obstruction through bulk dilatations, which supply the missing algebraic direction. We construct an asymptotically flat phase space of conformal gravity in which both types of Carroll-Weyl transformations and local Carroll boosts admit finite, integrable, and generically nonvanishing canonical charges, and derive their centrally extended algebra. Finally, we show that these central extensions arise from boundary anomalies through symplectic descent, yielding a gravitational prediction for Carroll-Weyl anomalies in flat holography.
ER -