# Typicality and thermality in 2d CFT

## TL;DR

This paper demonstrates that high energy eigenstates in 2D conformal field theories exhibit thermal behavior in their stress tensor correlations, linking typical states to black hole states in AdS3/CFT2 and exploring generalized ensembles for primary states.

## Contribution

It identifies typical high energy eigenstates as descendants and establishes their thermal correlation functions, clarifying their role in AdS3/CFT2 correspondence.

## Key findings

- Stress tensor correlators in typical states are thermal.
- Typical states correspond to descendants of high energy.
- Discrepancy between thermal and primary state correlators explained by generalized Gibbs ensemble.

## 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.