An investigation of AdS2 backreaction and holography

TLDR

The authors investigate a dilaton gravity model in AdS₂, develop a one‑dimensional effective description with a Schwarzian boundary action, and study black‑hole evaporation to explore entropy dynamics. They show the effective theory is equivalent to a one‑dimensional Liouville model, analyze its dynamics and symmetries via a canonical framework, and incorporate arbitrary conformal matter to study the resulting effective action with sources. The study finds that the Liouville‑equivalent model reproduces expected commutators of local operators at large time separations, matching the time shift from a gravitational shockwave, and reveals insights into entropy evolution during black‑hole evaporation.

Abstract

We investigate a dilaton gravity model in AdS2 proposed by Almheiri and Polchinski [1] and develop a 1d effective description in terms of a dynamical boundary time with a Schwarzian derivative action. We show that the effective model is equivalent to a 1d version of Liouville theory, and investigate its dynamics and symmetries via a standard canonical framework. We include the coupling to arbitrary conformal matter and analyze the effective action in the presence of possible sources. We compute commutators of local operators at large time separation, and match the result with the time shift due to a gravitational shockwave interaction. We study a black hole evaporation process and comment on the role of entropy in this model.