Shockwave S-matrix from Schwarzian quantum mechanics. (English) Zbl 1404.83076
Summary: Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in [T. G. Mertens et al., ibid. 2017, No. 8, Paper No. 136, 57 p. (2017; Zbl 1381.83089)]. We compare these results with bulk gravity expectations. We find that the semi-classical limit of the OTO four-point function exactly matches with the scattering amplitude obtained from the Dray-’t Hooft shockwave \( \mathcal{S} \)-matrix. We show that the two point function of heavy operators reduces to the semi-classical saddle-point of the Schwarzian action. We also explain a previously noted match between the OTO four point functions and 2D conformal blocks. Generalizations to higher-point functions are discussed.
MSC:
| 83C80 | Analogues of general relativity in lower dimensions |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 83C57 | Black holes |
| 81S10 | Geometry and quantization, symplectic methods |
Citations:
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