论文标题
Jackiw-teitelboim量子重力有缺陷和Aharonov-bohm效应
Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
论文作者
论文摘要
我们研究了在欧几里得二维负面弯曲背景上具有普遍性DiLATON潜力的Jackiw-Teitelboim重力理论。广义DILATON电位的作用是在二维流形上诱导锥形缺陷。我们表明，在存在恒定背景磁场和纯尺度aharonov-bohm场的情况下，该理论可以写入双曲线磁盘上带电粒子的普通量子力学。这张照片使我们能够准确计算相应重力动力学的波形和传播器。通过这种方法，我们能够重现状态的重力密度，并计算Hartle-Hawking状态的Réyni和纠缠熵。当我们在高温下重现经典熵时，我们也发现了在低温下占主导地位的额外拓扑作用。然后，我们展示缺陷的存在如何修改相关函数，包括超时订购的相关性，并减少Lyapunov指数。这是两种方法：通过直接量化边界施瓦兹理论，并通过尺寸降低$ sl（2，\ mathbb {z}）$黑洞。
We study the theory of Jackiw-Teitelboim gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the two-dimensional manifold. We show that this theory can be written as the ordinary quantum mechanics of a charged particle on a hyperbolic disk in the presence of a constant background magnetic field plus a pure gauge Aharonov-Bohm field. This picture allows us to exactly calculate the wavefunctions and propagators of the corresponding gravitational dynamics. With this method we are able to reproduce the gravitational density of states as well as compute the Réyni and entanglement entropies for the Hartle-Hawking state. While we reproduce the classical entropy at high temperature, we also find an extra topological contribution that becomes dominant at low temperatures. We then show how the presence of defects modify correlation functions, including the out-of-time-ordered correlation, and decrease the Lyapunov exponent. This is achieved two ways: by directly quantizing the boundary Schwarzian theory and by dimensionally reducing $SL(2,\mathbb{Z})$ black holes.
