JT gravity and deformed CFTs

We propose alternative \textit{UV completion} of pure JT gravity as well as CFT coupled to JT gravity, via a class of \textit{deformed} 2D CFT. In AdS/CFT with a prescribed classical limit, pure JT gravity in \textit{one-sided} AdS$_{2}$ black hole is argued to be described by certain holographic deformed CFT on a strip. Equivalently, these deformed CFTs can be recast as CFTs on one-sided AdS$_{2}$ black hole with \textit{emergent conformal boundary condition on a stretched horizon}$-$providing a \textit{proper UV frame} of JT gravity. On the other hand, JT gravity coupled to CFT with fixed central charge of $\mathcal{O}(1)$, is also described by deformed CFT on strip satisfying conformal boundary condition, with a different classical limit. The resulting CFT Hilbert spaces in both of the above classical limits yield the black hole entropy as thermal entropy and the high-energy density of states match that of JT gravity with a precise energy scale correspondence. Moreover, the Hilbert space defined for a two-sided black hole factorizes into two one-sided sectors in both limits. Notably in the second limit, degenerate zero modes of the deformed Hamiltonian$-$characterized by conformal primaries localized at the horizon$-$appear as a residual effect of the stretched horizon boundary condition. Exploiting the second limit, we compute entanglement entropy in one-dimensional quantum systems dual to a conformally glued black hole$-$Poincar\'e geometry in JT gravity, reproducing a `Page curve' via the quantum extremal surface prescription, with `Page time' set by the stretched horizon cutoff.