Infinite-dimensional conformal symmetry in two dimensions renders conformal field theories integrable with an infinite hierarchy of quantum KdV charges being in involution. These charges govern the structure of Virasoro descendant states and provide correct formulation for the Eigenstate Thermalization in 2d theories. After covering recent results on Eigenstate Thermalization, I will talk about an ongoing progress of calculating the spectrum of quantum KdV charges and generalized partition function of two dimensional theories in the limit of large central charge. The talk is based on https://arxiv.org/abs/1903.03559 as well as https://arxiv.org/abs/1812.05108 and https://arxiv.org/abs/1810.11025
Vasily Pestun
