The holographic dual of double scaled SYK

I will discuss a recent paper with Thomas Mertens and Jacopo Papalini where we establish a precise holographic duality between 2d sine dilaton gravity and DSSYK.  The role of the chord number in DSSYK is played by the (Weyl rescaled) geodesic length in the bulk. The most puzzling aspect of reconciling DSSYK with a simple gravitational dual at the classical level is the distinction between temperature and “fake temperature”. Equivalently, the entropy of DSSYK deviates at leading order from the Bekenstein-Hawking formula for black hole entropy. I will clarify how this arises from a constraint that the chord number is positive. Semi-classically, in sine dilaton gravity this translates to the insertion of a defect, from which it follows that fake temperature is the Hawking temperature of a smooth Lorentzian black hole. One remarkable feature is that in sine dilaton gravity quantization discretizes spacetime, therefore the Hilbert space is discrete.