2017/05/23 by Thomas G. Mertens, Gustavo J. Turiaci, Herman L. Verlinde · 2 voices · 21 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #cond-mat.str-el #hep-th
paper · pdf · doi:10.1007/jhep08(2017)136
46 pages + appendices. v2: typos corrected, references added. v3: matches published version
arxiv published 2017/05/23 · openalex created_date 2017/06/05 · openalex publication_date 2017/08/01 · arxiv created 2017/09/26 · arxiv updated 2017/09/28 · openalex updated_date 2026/07/28
We obtain exact expressions for a general class of correlation functions in the 1D quantum mechanical model described by the Schwarzian action, that arises as the low energy limit of the SYK model. The answer takes the form of an integral of a momentum space amplitude obtained via a simple set of diagrammatic rules. The derivation relies on the precise equivalence between the 1D Schwarzian theory and a suitable large c limit of 2D Virasoro CFT. The mapping from the 1D to the 2D theory is similar to the construction of kinematic space. We also compute the out-of-time ordered four point function. The momentum space amplitude in this case contains an extra factor in the form of a crossing kernel, or R-matrix, given by a 6j-symbol of SU(1,1). We argue that the R-matrix describes the gravitational scattering amplitude near the horizon of an AdS2 black hole. Finally, we discuss the generalization of some of our results to \cal N=1 and \cal N=2 supersymmetric Schwarzian QM.