  Many-body localization transition in a periodically driven quantum system is
investigated using a solution of a matching Bethe lattice problem for Floquet
states of a quantum random energy model with a generalization to more realistic
settings. It turns out that an external periodic field can both suppress and
enhance localization depending on field amplitude and frequency which leads to
three distinguishable regimes of field enhanced, controlled and suppressed
delocalization. The results can be verified experimentally in systems of cold
atoms and/or interacting spin defects in semiconductors.
