Probing sine dilaton gravity with flow central charge

We construct a holographic c-function for sine dilaton gravity (sDG) in the domain wall gauge. We show the equivalence between sDG and the two copies of Liouville conformal field theory (LCFT) and compute the associated central charge. We reproduce the central charge of LCFT from the holographic c-function of sDG corresponding to the UV limit. In contrast, in the deep IR limit, the c-function flows to the pure JT gravity, where the central charge becomes identically zero.