Melonic ladder holography with a single free bulk field in AdSd+1
Abstract
We derive a cylinder from the pair Casimir of a CFTd: at zero centre momentum it depends only on relative dilations and rotations. Relative-coordinate radial quantisation then encodes exchanged family labels as cylinder energies. For a melonic CFTd in the normalisable and stable range, the reduced ladder sum is the Robin boundary-to-boundary propagator of a single free scalar field in rigid AdSd+1, with the cylinder as its conformal boundary. The Robin boundary condition and bulk regularity (or parity) determine the holographic radial extension of the boundary data. A nonzero Robin boundary coefficient in global AdS breaks 2d AdS generators, yet the scalar's boundary propagator still encodes the conformal data of the melonic ladder. We demonstrate the correspondence for the Sachdev--Ye--Kitaev and the d=2 disorder-free long-range Amit--Roginsky melonic models, which correspond to a single free local scalar in AdS2 and AdS3, respectively.
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BibTeX
@misc{thong2026melonic,
title = {{Melonic ladder holography with a single free bulk field in AdS$_d+1$}},
author = {Kok Hong Thong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31989},
eprint = {2610.31989},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31989},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Melonic ladder holography with a single free bulk field in AdS_d+1
AU - Kok Hong Thong
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31989
UR - https://arxiv.org/abs/2610.31989
AB - We derive a cylinder from the pair Casimir of a CFT_d: at zero centre momentum it depends only on relative dilations and rotations. Relative-coordinate radial quantisation then encodes exchanged family labels as cylinder energies. For a melonic CFT_d in the normalisable and stable range, the reduced ladder sum is the Robin boundary-to-boundary propagator of a single free scalar field in rigid AdS_d+1, with the cylinder as its conformal boundary. The Robin boundary condition and bulk regularity (or parity) determine the holographic radial extension of the boundary data. A nonzero Robin boundary coefficient in global AdS breaks 2d AdS generators, yet the scalar's boundary propagator still encodes the conformal data of the melonic ladder. We demonstrate the correspondence for the Sachdev--Ye--Kitaev and the d=2 disorder-free long-range Amit--Roginsky melonic models, which correspond to a single free local scalar in AdS_2 and AdS_3, respectively.
ER -