  A quantum critical system described at low energy by a conformal field theory
(CFT) and subjected to a time-periodic boundary drive displays multiple
dynamical regimes depending on the drive frequency. We compute the behavior of
quantities including the entanglement entropy and Loschmidt echo, confirming
analytic predictions from field theory by exact numerics on the transverse
field Ising model, and demonstrate universality by adding non-integrable
perturbations. The dynamics naturally separate into three regimes: a
slow-driving limit, which has an interpretation as multiple quantum quenches
with amplitude corrections from CFT; a fast-driving limit, in which the system
behaves as though subject to a single quantum quench; and a crossover regime
displaying heating. The universal Floquet dynamics in all regimes can be
understood using a combination of boundary CFT and Kibble-Zurek scaling
arguments.
