Semiclassical correlators in Jackiw-Teitelboim gravity

In the semiclassical approximation to JT gravity, we find two-point and four-point correlators of heavy operators. To do so, we introduce a massive particle in the bulk and compute its action with gravitational backreaction. In Euclidean signature, the two-point function has a finite limit at large distances. In real time, we find that the thermal two-point function approaches an exponentially small value $\sim \exp(-N)$ at long time. We also find that after a period of exponential decay, the out of time ordered four-point function approaches an exponentially small value as well.