AI 中文总结
研究德西特时空标量场的四点OTOC，用程函近似，考虑任意维度和体质量。树图水平得最大李雅普诺夫指数，圈图有红外问题，正则化后简单配置下主导答案变化，微扰OTOC初增长，由引力子传播子大微分同胚介导。
AI 中文摘要
我们利用围绕德西特背景的引力的程函近似研究标量场的四点非时序关联函数（OTOC）。它可以通过为观察者装扮算符以规范不变的方式定义。我们考虑任意维度的德西特空间以及标量场的任意体质量。在树图水平，我们发现最大李雅普诺夫指数为$2\pi/\beta_{\rm dS}$。然而，我们描述了在圈图水平此计算中与引力子传播子矢量部分相关的红外问题。对该发散进行正则化导致牛顿常数渐近展开中所有奇次幂消失，所以在简单算符配置下主导答案是最大李雅普诺夫指数的两倍。我们发现德西特中的微扰OTOC最初会增长，这是混沌的量子界所不允许的。有趣的是，我们发现这种增长是由引力子传播子中的大微分同胚介导的。
英文摘要
We study the 4-point out-of-time-ordered correlator (OTOC) of scalar fields using the eikonal approximation to gravity around a de Sitter background. It can be defined in a gauge-invariant way by dressing the operators to an observer. We consider de Sitter space in any dimension and any bulk masses of the scalar fields. At tree level we find the maximal Lyapunov exponent of $2 π/β_{\rm dS}$. However, we describe an IR problem in this calculation at the loop level associated with the vector part of the graviton propagator. Regularizing this divergence leads to the vanishing of all odd powers in Newton's constant in the asymptotic expansion, so that the leading answer comes with twice the maximal Lyapunov exponent in simple operator configurations. We find that the perturbative OTOC in de Sitter can initially grow, which is not allowed by the quantum bound on chaos. Interestingly, we find that this growth is mediated by large diffeomorphisms in the graviton propagator.
Comments38 pages + appendices, 7 figures
