Jackiw-Teitelboim gravity and the models of a 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 fields. The background solutions corresponding to the $D=2$ 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 interpolating vacuum solution with AdS₂ in the IR and Lifshitz₂ in the UV (which serves as the thermal radiation background for our analysis) and (ii) the charged 2D black hole solution exhibiting Lifshitz₂ asymptotics. The analysis on thermal stability reveals the onset of a first-order phase transition at T~T₀ such that for T<T₀ the only possible state is the thermal radiation background without any black hole. On the other hand, as the temperature is gradually increased beyond a certain crossover value T~T₂(>T₀), an emerging globally stable black-hole-dominated phase has been observed which clearly indicates the onset of a Hawking-Page transition in 2D gravity models.