  Cardy has recently observed that certain carefully tuned states of 1+1 CFTs
on a timelike strip are periodic with period set by the light-crossing time.
The states in question are defined by Euclidean time evolution of conformal
boundary states associated with the particular boundary conditions imposed on
the edges of the strip. We explain this behavior, and the associated lack of
thermalization, by showing that such states are Lorentz-signature conformal
transformations of the strip ground state. Taking the long-strip limit implies
that states used to model thermalization on the Minkowski plane admit
non-thermal conformal extensions beyond future infinity of the Minkowski plane,
and thus retain some notion of non-thermal behavior at late times. We also
comment on the holographic description of these states.
