  Conformal field theories (CFT) play an important role in quantum field
theories as they allow for exact studies that are hard to access without the
conformal symmetries in place. A remarkable recent development is the
application of conformal field theory to periodically driven systems, the
so-called Floquet-driven CFTs. A number of recent works have found that there
are classes of periodically driven (1+1)-dimensional CFTs that can be
analytically solved, and that show both heating and non-heating phases, as well
as unusual properties in terms of information scrambling. Hitherto, most
results have focused on the dynamics of such models at stroboscopic times, i.e.
samples taken at each period of the time evolution. In this paper, we consider
time-evolution at arbitrary real times and derive formulas for the exact
time-propagation of heating and non-heating classes of Floquet-driven CFTs.
This requires a subtle treatment of non-stroboscopic time that leads to
different interpretations in terms of curved space-time dynamics in these
systems compared to previous results in the literature.
