DSSYK中虫洞长度的三圈 onset
Three-loop onset of the wormhole length in DSSYK
浏览论文内容
中文总结 AI 辅助
该研究计算了 DSSYK 模型中 t=0 时刻任意逆温度下虫洞长度的三圈 onset 值，扩展了已知结果，明确了加性常数的微观判定，还得到了长度方差和三阶累积量的两圈半经典展开式。
中文摘要 AI 辅助
在圆盘层面的 sine-dilaton 引力中，爱因斯坦-罗森桥的长度等于其对偶的双重标度 SYK（DSSYK）模型的 Krylov 扩散复杂度，其中双重标度参数 λ 控制半经典展开。我们在 t=0 时刻、任意逆温度 β 的热场双态中，计算了 onset 值 L₀ 的三圈闭合形式，扩展了已知的单圈结果。L₀ 代表初始热 Hartle-Hawking 态的制备复杂度，在 DSSYK 中，L₀ 等于 λ 乘以热态的平均弦数，为原本仅由全息重整化方案选择确定的加性常数提供了微观、明确的判定。两圈贡献来自 DSSYK 两点函数在重合插入点处的鞍点计算，其中各自发散的贡献仅在求和时抵消。在三圈层面，我们使用精确递推关系绕过鞍点分析，该关系可低成本生成长的高温展开式，通过大量独立数据点对提出的 Ansatz 进行修正和检验。最后，在低温 regime 下，每圈阶贡献一个额外的 β 幂次，将半经典级数重组为 Schwarzian 耦合 λβ 的展开式，我们通过独立的单圈 Schwarzian 计算验证了其主系数。将相同方法应用于 t=0 时刻的长度方差和三阶累积量，可得到它们的半经典两圈展开式。
英文摘要
The length of the Einstein-Rosen bridge in sine-dilaton gravity at disk level equals the Krylov spread complexity of the dual double-scaled SYK (DSSYK) model, with the double-scaling parameter $λ$ controlling the semiclassical expansion. We compute the onset value, $L_{0}$, in the thermofield double state at $t=0$ and arbitrary inverse temperature $β$, through three loops and in closed form, extending the known one-loop result. The quantity $L_{0}$ represents the preparation complexity of the initial thermal Hartle-Hawking state. In DSSYK, $L_{0}$ is $λ$ times the average chord number of the thermal state, providing a microscopic, unambiguous determination of an additive constant otherwise fixed only by a choice of holographic renormalization scheme. The two-loop contribution follows from a saddle point evaluation of the DSSYK two-point function at coincident insertion points, where individually divergent contributions cancel only in their sum. At three loops, we bypass the saddle point analysis using an exact recursion relation that generates long high-temperature expansions at low cost, fixing and testing a proposed Ansatz against many independent data points. Finally, in the low-temperature regime each loop order contributes one further power of $β$, reorganizing the semiclassical series into an expansion in the Schwarzian coupling $λβ$, whose leading coefficient we check against an independent one-loop Schwarzian computation. The same methods, applied to the length variance and third-order cumulant at $t=0$, give their semiclassical expansion through two loops.
