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

TL;DR

This work embeds matter into a boundary Liouville framework derived from a two-Liouville (or $H_3^+$-WZW) description of quantum gravity on a fixed boundary, establishing a duality between point-particle sources and scalar propagators via Liouville correlators. It derives quantum-corrected boundary entropy that matches EFT-like corrections (logarithmic and inverse-area terms) and demonstrates a boundary-originating modification to Hawking radiation, with a heuristic Page-like curve emerging from the evolution of boundary momentum content $P^2$. The results suggest a predictive, boundary-centric approach to quantum gravity where information about the interior leaks onto the horizon, and the entropy can be expressed in a Barvinsky-Vilkovisky-type expansion with fixed coefficients. The framework accommodates free and interacting scalar matter, offers insights into information flow across the horizon, and points to extensions to spinful fields and more general matter content.

Abstract

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.

Figures (1)

• Figure 1: Schematic plot of our Page-like curve (in blueish color) versus the Bekenstein-Hawking entropy (in orange). The momentum content of the horizon is plotted in green and agrees with our assumptions.