Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 8, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP08(2017)136
Keywords
2D Gravity; AdS-CFT Correspondence; Conformal Field Theory; Field Theories in Lower Dimensions
Categories
Funding
- Research Foundation-Flanders (FWO Vlaanderen)
- NSF [PHY-1620059]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1620059] Funding Source: National Science Foundation
Ask authors/readers for more resources
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 AdS 2 black hole. Finally, we discuss the generalization of some of our results to N = 1 and N = 2 supersymmetric Schwarzian QM.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available