Eigenstate Thermalization and 2d CFTs

Eigenstate Thermalization Hypothesis (ETH) is the idea that individual energy eigenstate of a sufficiently complex “chaotic” many-body quantum system exhibits thermal properties. This hypothesis is well confirmed in numerical experiments, however, analytically it is poorly understood.
We present analytic study of ETH in case of 2d CFTs. We will show how to calculate spectrum of all quantum KdV charges at large central charge limit. Given the spectrum we calculate the partition function of 2d CFTs decorated by higher quantum KdV charges at large central charge. Finally, we propose and check analytically that in the thermodynamic limit large central charge 2D CFTs satisfy generalized version of ETH, with the values of quantum KdV charges forming a complete set of thermodynamically relevant quantities, which unambiguously determine expectation values of all local observables from the vacuum family.