  We consider the late time behavior of the analytically continued partition
function $Z(\beta + it) Z(\beta - it)$ in holographic $2d$ CFTs. This is a
probe of information loss in such theories and in their holographic duals. We
show that each Virasoro character decays in time, and so information is not
restored at the level of individual characters. We identify a universal
decaying contribution at late times, and conjecture that it describes the
behavior of generic chaotic $2d$ CFTs out to times that are exponentially large
in the central charge. It was recently suggested that at sufficiently late
times one expects a crossover to random matrix behavior. We estimate an upper
bound on the crossover time, which suggests that the decay is followed by a
parametrically long period of late time growth. Finally, we discuss integrable
theories and show how information is restored at late times by a series of
characters. This hints at a possible bulk mechanism, where information is
restored by an infinite sum over non-perturbative saddles.
