  The Kitaev model on the honeycomb lattice is a paradigmatic system known to
host a wealth of nontrivial topological phases and Majorana edge modes. In the
static case, the Majorana edge modes are nondispersive. When the system is
periodically driven in time, such edge modes can disperse and become chiral. We
obtain the full phase diagram of the driven model as a function of the coupling
and the driving period. We characterize the quantum criticality of the
different topological phase transitions in both the static and driven model via
the notions of Majorana-Wannier state correlation functions and
momentum-dependent fidelity susceptibilities. We show that the system hosts
cross-dimensional universality classes: although the static Kitaev model is
defined on a 2D honeycomb lattice, its criticality falls into the universality
class of 1D linear Dirac models. For the periodically driven Kitaev model,
besides the universality class of prototype 2D linear Dirac models, an
additional 1D nodal loop type of criticality exists owing to emergent
time-reversal and mirror symmetries, indicating the possibility of engineering
multiple universality classes by periodic driving. The manipulation of
time-reversal symmetry allows the periodic driving to control the chirality of
the Majorana edge states.
