JT gravity and the models of Hawking-Page transition for 2D black holes

We propose a top down construction for Jackiw-Teitelboim (JT) gravity using compactification of $D=5$ gravity theories in the presence of Abelian ($U(1)$) as well as $SU(2)$ Yang-Mills (YM) fields. The background solutions corresponding to $D=2$ model have been obtained in the perturbative regime of the theory where the corrections have been estimated over the uncharged JT solutions while treating the gauge couplings as the parameters of the expansion. Our analysis reveals the existence of two classes of solutions namely, (i) the \emph{interpolating} vacuum solution with AdS$_2$ in the IR and Lifshitz$_2$ in the UV (which serves as the thermal radiation background for our analysis) and (ii) the charged 2D black hole solution exhibiting Lifshitz$_2$ asymptotics. The analysis on thermal stability reveals the onset of a first order phase transition at $T \sim T_0$ such that for $T < T_0$ the only possible state is the thermal radiation background without any black hole. On the other hand, as the temperature is gradually increased beyond certain \emph{crossover} value $T\sim T_2 (>T_0 )$, an emerging \emph{globally} stable black hole dominated phase has been observed which clearly indicates the onset of Hawking-Page (HP) transition in 2D gravity models.