Abstract
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 ∼ 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.
Highlights
The Schwarzian action can be found directly from the SYK [1]
We find that the thermal two-point function approaches an exponentially small value ∼ exp(−N ) at long time
In the Euclidean case, when the length scale in the N CF T goes to infinity, the length of the relevant geodesic that appears in the correlator approaches a finite limit, and the two-point function approaches a limit as well
Summary
With A being the area of the black hole horizon This action belongs to a family of dilaton gravity models studied extensively in [23]. We can think of G as the coupling coming from dimensional reduction of the four-dimensinal action (2.5), and the semiclassical regime is defined by G 1 In our definition, it means that we always consider the boundary value of the dilaton to be large, φb 1. The boundary of the N AdS space is at finite distance from the “center” of the true AdS2, and has a finite length This allows us to study the boundary theory using the gravitational action only. The same Schwarzian term appears in the effective action of the SYK model as the first correction to the conformal answer This allows us to tentatively identify the parameters of the two theories as: φr(JT) ∼. Our goal is to find the full semiclassical answer for the two-point function, taking this back-reaction into account
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