Typicality and thermality in 2d CFT

Abstract

We identify typical high energy eigenstates in two-dimensional conformal field theories at finite c and establish that correlation functions of the stress tensor in such states are accurately thermal as defined by the standard canonical ensemble. Typical states of dimension h are shown to be typical level h/c descendants. In the AdS3/CFT2 correspondence, it is such states that should be compared to black holes in the bulk. We also discuss the discrepancy between thermal correlators and those computed in high energy primary states: the latter are reproduced instead by a generalized Gibbs ensemble with extreme values chosen for the chemical potentials conjugate to the KdV charges.