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We consider a clean quantum system subject to strong periodic driving. Theexistence of a dominant energy scale, $h_D^x$, can generate considerablestructure in an effective description of a system which, in the absence of thedrive, is non-integrable, interacting, and does not host localization. Inparticular, we uncover points of freezing in the space of drive parameters(frequency and amplitude). At those points, the dynamics is severelyconstrained due to the emergence of an almost exact local conserved quantity,which scars the {\it entire} Floquet spectrum by preventing the system fromheating up ergodically, starting from any generic state, even though itdelocalizes over an appropriate subspace. At large drive frequencies, where ana\"ive Magnus expansion would predict a vanishing effective (average) drive,we devise instead a strong-drive Magnus expansion in a moving frame. There, theemergent conservation law is reflected in the appearance of an `integrability'of an effective Hamiltonian. These results hold for a wide variety ofHamiltonians, including the Ising model in a transverse field in {\it anydimension} and for {\it any form of Ising interactions}. The phenomenon is alsoshown to be robust in the presence of {\it two-body Heisenberg interactionswith any arbitrary choice of couplings}. Further, we construct a real-timeperturbation theory which captures resonance phenomena where the conservationbreaks down, giving way to unbounded heating. This opens a window on thelow-frequency regime where the Magnus expansion fails.

Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws