In this paper, based on RT formula, by identifying the pure state UV and IR entanglement entropies of a perturbed CFT$_2$ with geodesic lengths in the bulk, we demonstrate that the dual geometry is uniquely determined to be asymptotically AdS$_3$. The pure AdS$_3$ geometry is recovered by taking the massless limit of the system. Our derivations hold in both static and covariant scenarios.
Categories: hep-th cond-mat.stat-mech gr-qc quant-ph