Peng Wang, Houwen Wu, Haitang Yang

How to construct the $d+1$ dimensional geometry explicitly from the dual CFT$_d$ is a widely concerned problem. Specifically, given entanglement entropies of a CFT$_2$, which is purely expressed by two dimensional parameters, can we build the dual three dimensional geometry unambiguously? To do this, one must assume nothing is known about the three dimensional geometry and starts with the most general setup. In this paper, by identifying the UV and IR entanglement entropies of a perturbed usual CFT$_2$ with the geodesic lengths, we show that, the dual geometry is uniquely determined to be asymptotic AdS$_3$. The hidden dimension is generated by the energy cut-off of the CFT$_2$, according to the holographic principle. The pure AdS$_3$ is obtained by taking the massless limit. Our derivations apply to both static and covariant scenarios. Moreover, what deserves special attention is that the ratio of the numberical factors of the UV/IR entanglement entropies are crucial to have a dual geometry. We are led to conjecture a necessary condition of holographic CFT$_2$.

Juan Maldacena, Xiao-Liang Qi

We construct a nearly-$AdS_2$ solution describing an eternal traversable wormhole. The solution contains negative null energy generated by quantum fields under the influence of an external coupling between the two boundaries. In parallel, we discuss two SYK systems coupled by a relevant interaction. The physics of the two cases is very similar. They both share a "gravitational" subsector which is identical. The solution within this subsector sets the stage for dynamics which is almost conformal invariant. We study this system in detail, both in gravity and in the SYK model. The coupled SYK models have an interesting phase diagram at finite temperature, displaying the usual Hawking-Page transition between the thermal AdS phase at low temperature and the black hole phase at high temperature. Interestingly, these two phases are continuously connected in the microcannonical ensemble.