Typicality and thermality in 2d CFT
arXiv:1904.00668 · doi:10.1007/JHEP07(2019)143
The paper shows that typical high‑energy eigenstates in two‑dimensional conformal field theories have stress‑tensor correlation functions that match those of a canonical thermal ensemble, and discusses how primary states instead correspond to a generalized Gibbs ensemble with specific KdV charge potentials.
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 AdS$_3$/CFT$_2$ 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.
27 pages, 1 figure