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We provide the first steps toward a flat space holographic correspondence in two bulk spacetime dimensions. The gravity side is described by a conformally transformed version of the matterless Callan-Giddings-Harvey-Strominger model. The field theory side follows from the complex Sachdev-Ye-Kitaev model in the limit of large specific heat and vanishing compressibility. We derive the boundary action analogous to the Schwarzian as the key link between gravity and field theory sides and show that it coincides with a geometric action discovered recently by one of us H. R. Afshar, Warped Schwarzian theory, J. High Energy Phys. 02 (2020) 126.
Afshar et al. (2020) studied this question.