Why Cooper pairs live in AdS2: a spectral analysis of the Yukawa-SYK model
Abstract
We establish the spectral foundation of the geometric formulation of Cooper pairing in the Yukawa--Sachdev--Ye--Kitaev model. Starting from the large-N bilocal effective action, we derive the Gaussian fluctuation kernel in the even-frequency spin-singlet Cooper channel. Following the construction of Maldacena and Stanford, we determine the kernel eigenvalue k(h) analytically for arbitrary conformal weight h and resolve the pairing fluctuations into the continuous and discrete sectors of the associated de-Sitter space Laplacian. We show that the superconducting instability and the universal low-energy fluctuations near it reside entirely in the continuous scattering sector, while the discrete modes remain non-critical. Expanding the kernel about the lowest continuum mode yields a Klein--Gordon action on dS2, restricted to the continuous spectral subspace. This is precisely the subspace on which the inverse Radon transform to AdS2 is well defined. The projected bilocal Cooper-pair field can therefore be mapped onto a scalar matter field propagating in AdS2, without requiring any further spectral restriction on the bulk theory. Our results provide the missing microscopic justification for the projection implicit in earlier holographic formulations and clarify how a local bulk field emerges from the bilocal pairing theory.
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BibTeX
@misc{stangier2026cooper,
title = {{Why Cooper pairs live in AdS2: a spectral analysis of the Yukawa-SYK model}},
author = {Veronika Carolin Stangier and Jörg Schmalian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26251},
eprint = {2608.26251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Why Cooper pairs live in AdS2: a spectral analysis of the Yukawa-SYK model
AU - Veronika Carolin Stangier
AU - Jörg Schmalian
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2608.26251
UR - https://arxiv.org/abs/2608.26251
AB - We establish the spectral foundation of the geometric formulation of Cooper pairing in the Yukawa--Sachdev--Ye--Kitaev model. Starting from the large-N bilocal effective action, we derive the Gaussian fluctuation kernel in the even-frequency spin-singlet Cooper channel. Following the construction of Maldacena and Stanford, we determine the kernel eigenvalue k(h) analytically for arbitrary conformal weight h and resolve the pairing fluctuations into the continuous and discrete sectors of the associated de-Sitter space Laplacian. We show that the superconducting instability and the universal low-energy fluctuations near it reside entirely in the continuous scattering sector, while the discrete modes remain non-critical. Expanding the kernel about the lowest continuum mode yields a Klein--Gordon action on dS_2, restricted to the continuous spectral subspace. This is precisely the subspace on which the inverse Radon transform to AdS_2 is well defined. The projected bilocal Cooper-pair field can therefore be mapped onto a scalar matter field propagating in AdS_2, without requiring any further spectral restriction on the bulk theory. Our results provide the missing microscopic justification for the projection implicit in earlier holographic formulations and clarify how a local bulk field emerges from the bilocal pairing theory.
ER -