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, ℤ) black holes.

我们研究了欧几里得二维负弯曲背景下具有广义狄拉顿势的Jackiw-Teitelboim重力理论。广义膨胀子势的作用是在二维流形上引起圆锥形缺陷。我们证明了该理论可以写为在恒定背景磁场加纯量规Aharonov-Bohm场的存在下，双曲圆盘上带电粒子的普通量子力学。这张图片使我们能够精确地计算出相应的引力动力学的波函数和传播子。使用这种方法，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，我们还发现在低温下占主导地位的额外拓扑贡献。然后，我们显示缺陷的存在如何修改相关函数，包括无序相关，并降低Lyapunov指数。这可以通过两种方式实现：通过直接量化边界Schwarzian理论和通过降维SL（2， ℤ）黑洞。