A folded string dual for the Sachdev-Ye-Kitaev model

We propose a folded string moving in rigid AdS$_2$ with imaginary radius squared as a dual of the Sachdev-Ye-Kitaev (SYK) model at its conformal fixed point. In standard AdS$_2$, the string is represented by two massless particles connected by straight string segments. The particles move at the speed of light, abruptly reversing direction at turning points. We describe the system using the lightcone coordinates of these points, with the Poisson structure obtained from the Peierls bracket. In AdS$_2$ with imaginary radius squared, quantization of the string's mass-squared in momentum-fraction space yields a P\"oschl-Teller equation, reproducing the SYK operator spectrum.