Landau and fractionalized theories of periodically driven intertwined orders

We obtain the phase diagrams of field theories of intertwined orders in the presence of periodic driving by an external field which preserves all symmetries. We consider both a conventional Landau theory of competing orders, and a fractionalized theory in which the order parameters are distinct composites of an underlying multi-component Higgs field. We work in the large $N$ limit and couple to a Markovian bath. The long time limits are characterized by non-zero average values, oscillations with the drive period and/or half the drive period, quasi-periodic oscillations, or chaotic behavior.