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.

A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N ) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories.The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.

Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens’ principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens’ principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.