For systems with projective symmetry representations, the paper proposes a modified ETH and shows that charged operators with symmetry-supplied charges thermalize to a generalized Gibbs ensemble, not the ordinary Gibbs ensemble.
Comments on Thermalization in 2D CFT
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abstract
We revisit certain aspects of thermalization in 2D CFT. In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a BTZ black hole. The extra conserved charges, while rendering $c < 1$ theories essentially integrable, therefore seem to have little effect on large-$c$ conformal field theories.
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Eigenstate Thermalization Hypothesis with projective representation
For systems with projective symmetry representations, the paper proposes a modified ETH and shows that charged operators with symmetry-supplied charges thermalize to a generalized Gibbs ensemble, not the ordinary Gibbs ensemble.