Holographic central charge for double scaled SYK

Abstract: In this paper, we calculate the holographic central charge ($c_{sDG}$) associated with sine dilaton gravity in the semiclassical limit. Following the standard holographic folklore, this should correspond to the central charge associated with a $q$ Schwarzian quantum mechanical model in the double scaling limit. In the low energy limit, the gravity description flows into the ordinary JT gravity which is a conjectured dual of ordinary Schwarzian quantum mechanics at strong coupling. We compute the associated central charge ($c_{JT}$), which reveals $c_{sDG}>c_{JT}$. We identify this as an artifact of the UV completion of JT gravity in terms of sine dilaton gravity.