On periodically driven AdS/CFT

TL;DR

This paper uses AdS/CFT to analyze how a four-dimensional conformal field theory responds to periodic external driving, focusing on energy dissipation, thermalization, and entanglement dynamics in the dual gravitational description.

Contribution

It provides a detailed holographic study of energy dissipation and thermalization delays in a periodically driven CFT, including backreaction effects and horizon evolution.

Findings

Energy dissipation depends on frequency and operator dimension.

Thermalization of entanglement entropy is delayed proportionally to region size.

Horizon area increase matches entropy production.

Abstract

We use the AdS/CFT correspondence to study a thermally isolated conformal field theory in four dimensions which undergoes a repeated deformation by an external periodic time-dependent source coupled to an operator of dimension Delta. The initial state of the theory is taken to be at a finite temperature. We compute the energy dissipated in the system as a function of the frequency and of the dimension Delta of the perturbing operator. This is done in the linear response regime. In order to study the details of thermalization in the dual field theory, the leading-order backreaction on the AdS black brane metric is computed. The evolution of the event and the apparent horizons is monitored; the increase of area in each cycle coincides with the increase in the equilibrium entropy corresponding to the amount of energy dissipated. The time evolution of the entanglement entropy of a spherical region and that of the two-points function of a probe operator with a large dimension are also inspected; we find a delay in the thermalization of these quantities which is proportional to the size of the region which is being probed. Thus, the delay is more pronounced in the infrared. We comment on a possible transition in the time evolution of the energy fluctuations.