Liouville theory on a horizon: point particle/scalar field duality and Page-like curve

We show that the consequences of a recent paper on quantum gravity are 1) a duality between point particles and massive scalar propagators, 2) the recovery of the entropy of a boundary (a black hole) in the same form as that of the EFT approach to Quantum Gravity and 3) a quantum correction to Hawking radiations and a Page-like curve. In this recent paper, information about what lies inside a boundary is encoded onto it, meaning that in this approach the information directly leaks from the horizon to the bulk in the form of Hawking radiations.