AdS3 Recursion Relations, Double Copy and CFT2 Ward Identities
Abstract
We consider correlation functions of massless fields in three-dimensional Anti-de Sitter spacetime. Using embedding-space spinors akin to spinor helicity variables, we show that masslessness implies holomorphicity. We perform a deformation of the spinors, analogous to the BCFW shift for flat-space amplitudes, to bootstrap correlation functions of Chern-Simons theory in the bulk. We show that the resulting recursion relations in the bulk AdS3 are equivalent to the usual CFT2 Ward identities for the boundary conserved currents. The double copy of those recursion relations is equivalent to the Ward identities for the stress-energy tensor. Our findings illustrate how modern amplitude techniques can shed new light on CFT correlators, and provide a novel interpretation of fundamental results in two-dimensional conformal field theory.
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BibTeX
@misc{mathys2026ads3,
title = {{$\boldsymbol\rm AdS_3$ Recursion Relations, Double Copy and $\boldsymbol\rm CFT_2$ Ward Identities}},
author = {Grégoire Mathys and Guilherme L. Pimentel and Facundo Rost},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12046},
eprint = {2609.12046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12046},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - AdS_3 Recursion Relations, Double Copy and CFT_2 Ward Identities
AU - Grégoire Mathys
AU - Guilherme L. Pimentel
AU - Facundo Rost
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12046
UR - https://arxiv.org/abs/2609.12046
AB - We consider correlation functions of massless fields in three-dimensional Anti-de Sitter spacetime. Using embedding-space spinors akin to spinor helicity variables, we show that masslessness implies holomorphicity. We perform a deformation of the spinors, analogous to the BCFW shift for flat-space amplitudes, to bootstrap correlation functions of Chern-Simons theory in the bulk. We show that the resulting recursion relations in the bulk AdS_3 are equivalent to the usual CFT_2 Ward identities for the boundary conserved currents. The double copy of those recursion relations is equivalent to the Ward identities for the stress-energy tensor. Our findings illustrate how modern amplitude techniques can shed new light on CFT correlators, and provide a novel interpretation of fundamental results in two-dimensional conformal field theory.
ER -