Shockwave S-matrix from Schwarzian quantum mechanics

When the energy is of order C, the two-point correlator becomes thermal with an effective temperature, consistent with ETH.

“We can verify that when the energy is of order C, this correlator becomes thermal with an effective temperature , consistent with ETH, see section 6.2 of Lam et al. (2018).”

The heavy limit can be taken both directly in (3.24) or using the sourced saddle, with matching results.

“The limit can be taken both directly in the expression (3.24), or using the new sourced saddle, with matching results Lam et al. (2018).”

In the large C limit, only the pole at is relevant, and its residue gives a contribution to the OTOC amplitude (3.41).

“As shown in Lam et al. (2018), in this limit only the pole at is relevant. Its residue gives a contribution to the OTOC amplitude given by3.41”

The answer matches specific Virasoro vacuum blocks computed in Chen et al. (2017).

“This answer also matches with specific Virasoro vacuum blocks computed in Chen et al. (2017), for reasons explained in Lam et al. (2018).”

More complicated correlators can be computed by diagrammatic rules, which can compute any bilocal Schwarzian correlator or boundary correlators with quantum gravity effects.

“More complicated correlators can be computed by following a simple set of diagrammatic rules, developed in Mertens et al. (2017) and Lam et al. (2018). These can be used to compute any bilocal Schwarzian correlator, or equivalently the boundary correlators with quantum gravity effects.”