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Dirichlet gravitons in AdS4 and ℒΛw1+∞ wedge algebra

  • Hare Krishna
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Abstract

We derive the AdS deformation of the flat-space soft-graviton algebra with Dirichlet boundary conditions. Starting from the AdS4 spinor-helicity representation, we Mellin-transform linearized graviton solutions and construct the AdS wedge, including its Laurent completion. The Dirichlet boundary condition pairs opposite helicities, while AdS covariance fixes their relative normalization. Assuming linear closure and normalizing the global modes to reproduce the geometric AdS isometries, covariance and the Jacobi identities uniquely determine the soft-mode bracket. The result is the wedge of ℒΛw1+∞, where Λ=−ℓ−2. This provides a bulk derivation of the cosmological-constant deformation that incorporates the AdS boundary condition, without relying on collinear splitting functions or a self-dual truncation.

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Cite

BibTeXRIS
BibTeX
@misc{krishna2026dirichlet,
  title = {{Dirichlet gravitons in AdS$_4$ and $\mathcalL_Λw_1+\infty$ wedge algebra}},
  author = {Hare Krishna},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36764},
  eprint = {2609.36764},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36764},
}
RIS
TY  - UNPB
TI  - Dirichlet gravitons in AdS_4 and ℒ_Λw_1+∞ wedge algebra
AU  - Hare Krishna
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36764
UR  - https://arxiv.org/abs/2609.36764
AB  - We derive the AdS deformation of the flat-space soft-graviton algebra with Dirichlet boundary conditions. Starting from the AdS_4 spinor-helicity representation, we Mellin-transform linearized graviton solutions and construct the AdS wedge, including its Laurent completion. The Dirichlet boundary condition pairs opposite helicities, while AdS covariance fixes their relative normalization. Assuming linear closure and normalizing the global modes to reproduce the geometric AdS isometries, covariance and the Jacobi identities uniquely determine the soft-mode bracket. The result is the wedge of ℒ_Λw_1+∞, where Λ=−ℓ^−2. This provides a bulk derivation of the cosmological-constant deformation that incorporates the AdS boundary condition, without relying on collinear splitting functions or a self-dual truncation.
ER  -