变形双标SYK及从有限截断共形场论到达伸展视界
Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
AI总结：
本文研究基于有限截断共形场论的双标SYK模型在弦哈密顿变形下的性质，探讨了Krylov复杂度、热力学性质及纠缠熵等核心问题，通过变形实现Susskind的宇宙学伸展视界提案。
摘要：
我们研究基于有限截断共形场论的双标SYK（DSSYK）模型在弦哈密顿变形下的性质，适用于一般稀顿引力理论和狄利克特边界。该形式立即将T\ar{T}(+Λ_2)的低维类比变形T^2(+Λ_1)作为特殊情况。一般来说，变形混合了种子理论中的弦基态的希尔伯特空间，我们通过兰扎斯算法对其进行排序。所得到的Krylov复杂度代表了在bulk中的有限截断下的虫洞长度。我们研究变形理论的热力学性质；Krylov复杂度的增长；随物质弦的n点相关函数的演变；以及DSSYK模型双标代数之间在给定弦态下的纠缠熵。后者在三标缩放极限下表现为Ryu-Takayanagi公式下的bulk中的最小二维面积。通过在变形DSSYK的上尾能谱中进行T^2和T^2+Λ_1变形，我们具体实现了Susskind的宇宙学伸展视界提案。我们还讨论了其他扩展，包括正弦稀顿引力、终点膜和Almheiri-Goel-Hu模型。
英文摘要：
We study the properties of the double-scaled SYK (DSSYK) model under chord Hamiltonian deformations based on finite cutoff holography for general dilaton gravity theories with Dirichlet boundaries. The formalism immediately incorporates a lower-dimensional analog of $\text{T}\bar{\text{T}}(+Λ_2)$ deformations, denoted $T^2(+Λ_1)$, as special cases. In general, the deformation mixes the chord basis of the Hilbert space in the seed theory, which we order through the Lanczos algorithm. The resulting Krylov complexity for the Hartle-Hawking state represents a wormhole length at a finite cutoff in the bulk. We study the thermodynamic properties of the deformed theory; the growth of Krylov complexity; the evolution of $n$-point correlation functions with matter chords; and the entanglement entropy between the double-scaled algebras of the DSSYK model for a given chord state. The latter, in the triple-scaling limit, manifests as the minimal codimension-two area in the bulk following the Ryu-Takayanagi formula. By performing a sequence of $T^2$ and $T^2+Λ_1$ deformations in the upper tail of the energy spectrum in the deformed DSSYK, we concretely realize the cosmological stretched horizon proposal in de Sitter holography by Susskind. We discuss other extensions with sine dilaton gravity, end-of-the-world branes, and the Almheiri-Goel-Hu model.
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