An investigation of AdS 2 backreaction and holography
Julius Engelsöy (Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A., Physics Department, Royal Institute of Technology, 11428, Stockholm, Sweden); Thomas Mertens (Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A.); Herman Verlinde (Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, U.S.A., Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A.)
We investigate a dilaton gravity model in AdS 2 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.
