Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography
Abstract
We construct the bulk local states of a massive spin-1 field in AdS3/CFT2 and three-dimensional Carrollian holography. In AdS, covariance under the isometries that leave a bulk point invariant determines the three components of the vector there and splits the solution into two branches of definite helicity, whose inner products reproduce the massive vector two-point function of AdS3. By expanding the massive vector HKLL representation in boundary descendants, one can reproduce the three component states term by term. The two branches together describe the parity-invariant Proca field, and one alone the single propagating mode of Maxwell--Chern--Simons theory. The same conditions are solved in the induced representation of the Carrollian theory, where the solution again splits into two branches. Under the flat limit of the generators the highest weight module becomes the induced module, and the AdS states and Green's functions become their Carrollian counterparts, which supports the induced representation as the home of massive bulk excitations in Carrollian holography. This is the first bulk local state built with spin, complete from the state itself to its bulk-to-bulk propagator and to the limit relating the two descriptions.
Related
- Carrollian quantum states and flat space holography
- Lectures on Carrollian holography
- Carrollian Conformal Dynamics and Flat-Space Holography
- Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane
- Melonic ladder holography with a single free bulk field in AdSd+1
BibTeX
@misc{hao2026spin1,
title = {{Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography}},
author = {Peng-Xiang Hao and Kotaro Shinmyo and Kenta Suzuki and Yu-ki Suzuki and Shunta Takahashi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07548},
eprint = {2610.07548},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07548},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography
AU - Peng-Xiang Hao
AU - Kotaro Shinmyo
AU - Kenta Suzuki
AU - Yu-ki Suzuki
AU - Shunta Takahashi
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07548
UR - https://arxiv.org/abs/2610.07548
AB - We construct the bulk local states of a massive spin-1 field in AdS_3/CFT_2 and three-dimensional Carrollian holography. In AdS, covariance under the isometries that leave a bulk point invariant determines the three components of the vector there and splits the solution into two branches of definite helicity, whose inner products reproduce the massive vector two-point function of AdS_3. By expanding the massive vector HKLL representation in boundary descendants, one can reproduce the three component states term by term. The two branches together describe the parity-invariant Proca field, and one alone the single propagating mode of Maxwell--Chern--Simons theory. The same conditions are solved in the induced representation of the Carrollian theory, where the solution again splits into two branches. Under the flat limit of the generators the highest weight module becomes the induced module, and the AdS states and Green's functions become their Carrollian counterparts, which supports the induced representation as the home of massive bulk excitations in Carrollian holography. This is the first bulk local state built with spin, complete from the state itself to its bulk-to-bulk propagator and to the limit relating the two descriptions.
ER -