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PreprintCC BY 4.0arXiv

A Matrix View of Holographic Null-State Equations in d≥ 2

  • Kuo-Wei Huang
Open at sourcePDFDOICite

Abstract

We show that the null-state-type partial differential equations recently derived from AdS gravity with a black hole can be efficiently organized using finite-dimensional matrices with systematic off-diagonal structures. This matrix formulation generates an infinite tower of CFT differential equations at arbitrary levels. The d=2 matrix reproduces a known result based on Virasoro null-state vectors at large central charge and admits an algebraic representation in terms of a linear combination of the identity matrix and sl2 generators, with a heavy-state deformation encoding the central charge contribution. The d=4 governing matrix exhibits a similar yet richer structure involving products of sl2 generators. We also discuss recursion relations and factorized product structures associated with these holographic differential equations.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026matrix,
  title = {{A Matrix View of Holographic Null-State Equations in $d\geq 2$}},
  author = {Kuo-Wei Huang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02855},
  eprint = {2611.02855},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02855},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Matrix View of Holographic Null-State Equations in d≥ 2
AU  - Kuo-Wei Huang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02855
UR  - https://arxiv.org/abs/2611.02855
AB  - We show that the null-state-type partial differential equations recently derived from AdS gravity with a black hole can be efficiently organized using finite-dimensional matrices with systematic off-diagonal structures. This matrix formulation generates an infinite tower of CFT differential equations at arbitrary levels. The d=2 matrix reproduces a known result based on Virasoro null-state vectors at large central charge and admits an algebraic representation in terms of a linear combination of the identity matrix and sl_2 generators, with a heavy-state deformation encoding the central charge contribution. The d=4 governing matrix exhibits a similar yet richer structure involving products of sl_2 generators. We also discuss recursion relations and factorized product structures associated with these holographic differential equations.
ER  -