Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space

We study a two-dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near-extremal black holes, or more generally, nearly AdS 2 spacetimes. The asymptotic symmetries of AdS 2 are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the AdS 2 geometry and they are explicitly broken by the small deformation away from AdS 2 . This pattern of spontaneous plus explicit symmetry breaking governs the gravitational backreaction of the system. It determines several gravitational properties such as the linear in temperature dependence of the near-extremal entropy as well as the gravitational corrections to correlation functions. These corrections include the ones determining the growth of out-of-time-order correlators that is indicative of chaos. These gravitational aspects can be described in terms of a Schwarzian derivative effective action for a reparametrization. ........