论文标题
ADS $ _2 $字符串上的混乱和重新处理模式
Chaos and the reparametrization mode on the AdS$_2$ string
论文作者
论文摘要
我们研究了与ADS $ _2 $几何形状的开放式弦世界表散射相对应的全息相关器。在超级订单配置中，相关器显示出lyapunov的增长，使混乱融合。我们表明，在lyapunov制度和晚期指数衰减之间的双尺度限制中，可以准确地获得超阶相关器（OTOC），并且在JT重力中的类似计算中发现了相同的功能形式。结果可以理解为来自ADS $ _2 $黑洞的地平线附近的高能量散射，并且基本上由平面空间Worldsheet S-Matrix控制。虽然先前在ADS $ _2 $字符串上使用的作品主要采用了静态量规方法，但在这里，我们专注于保形规，并阐明边界重新分析在相关器计算中的作用。我们发现，修复模式由非本地作用控制，该动作与JT重力中产生的Schwarzian动作不同，尤其是导致$ SL（2，\ Mathbb {r}）$不变边界相关器。但是，双尺度极限中的OTOC具有与从Schwarzian获得的功能形式相同的功能形式，并且可以使用Reparametrized操作进行计算，并重新定义了预期在限制中占主导地位的图表的子集。我们结果的一种应用是由$ {\ cal n} = 4 $ sym定义的缺陷CFT。在这种情况下，我们表明，在双尺度限制中，OTOC的确切结果与最新的分析性自举预测在强耦合下针对三环阶的确切一致。
We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS$_2$ geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS$_2$ black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS$_2$ string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to $SL(2,\mathbb{R})$ invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in ${\cal N}=4$ SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.
