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The Conformal w-Algebra
Abstract
Einstein gravity in four asymptotically flat dimensions is governed by a tower of soft theorems obeying an ℒw1+∞ commutator algebra. This algebra is deformed to ℒΛw1+∞ in the conformally related AdS4 and dS4 spacetimes. Here we construct the larger ``conformal w-algebra", denoted 𝒞w1+∞, which acts on conformal gravity in all of these spacetimes. It includes ℒw1+∞, ℒΛw1+∞ and the so(4,2) 4D conformal algebra as subalgebras. We show that 𝒞w1+∞ is the conformal completion of either ℒw1+∞ or ℒΛw1+∞. A derivation of 𝒞w1+∞ is given as the symmetry of the twistor action of self-dual conformal gravity.
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BibTeX
@misc{heuveline2026conformal,
title = {{The Conformal $w$-Algebra}},
author = {Simon Heuveline and Nia Robles Del Pino and Andrew Strominger},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13381},
eprint = {2609.13381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13381},
}
RIS
TY - UNPB
TI - The Conformal w-Algebra
AU - Simon Heuveline
AU - Nia Robles Del Pino
AU - Andrew Strominger
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13381
UR - https://arxiv.org/abs/2609.13381
AB - Einstein gravity in four asymptotically flat dimensions is governed by a tower of soft theorems obeying an ℒw_1+∞ commutator algebra. This algebra is deformed to ℒ_Λw_1+∞ in the conformally related AdS_4 and dS_4 spacetimes. Here we construct the larger ``conformal w-algebra", denoted 𝒞w_1+∞, which acts on conformal gravity in all of these spacetimes. It includes ℒw_1+∞, ℒ_Λw_1+∞ and the so(4,2) 4D conformal algebra as subalgebras. We show that 𝒞w_1+∞ is the conformal completion of either ℒw_1+∞ or ℒ_Λw_1+∞. A derivation of 𝒞w_1+∞ is given as the symmetry of the twistor action of self-dual conformal gravity.
ER -