发表机构
Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology; Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所; 卡尔斯鲁厄理工学院量子材料与技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过对Yukawa-SYK模型的谱分析，为库珀对在AdS2中的存在提供了微观依据，明确了超导不稳定性相关涨落的谱性质，阐明了双域库珀对场与AdS2中标量物质场的映射关系。
AI 中文摘要
我们确立了Yukawa-Sachdev-Ye-Kitaev模型中库珀配对几何形式的谱基础。从大N双域有效作用量出发，我们推导了偶频自旋单态库珀通道中的高斯涨落核。遵循Maldacena和Stanford的构造，我们针对任意共形权重h解析地确定了核本征值k(h)，并将配对涨落分解为相关de Sitter空间拉普拉斯算子的连续与离散部分。我们证明，超导不稳定性及其附近的普适低能涨落完全处于连续散射部分，而离散模式保持非临界。将核在最低连续模式附近展开，得到了限制在连续谱子空间上的dS2上的Klein-Gordon作用量，该子空间正是对AdS2的逆Radon变换有良好定义的子空间。因此，投影后的双域库珀对场可映射为在AdS2中传播的标量物质场，无需对体理论施加进一步的谱限制。我们的结果为早期全息形式中隐含的投影提供了缺失的微观证明，并阐明了局部体场如何从双域配对理论中产生。
英文摘要
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 $k\left(h\right)$ 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 ${\rm dS}_2$, restricted to the continuous spectral subspace. This is precisely the subspace on which the inverse Radon transform to ${\rm AdS}_2$ is well defined. The projected bilocal Cooper-pair field can therefore be mapped onto a scalar matter field propagating in ${\rm AdS}_2$, 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.
Comments22 pages, 4 figures
