Three quantizations of conformal field theory

Needless to say, conformal field theory is elemental in the study of string theory, statistical quantum systems, and various quantum field theories.
Two-dimensional conformal field theory is usually quantized by the so-called radial quantization. However, this is not the only way. As a matter of fact, there are two other distinctive choices for the time foliation, or equivalently, the Hamiltonian. One of these choices yields the continuous Virasoro algebra, while the other choice leads to the Virasoro algebra on a torus. The former case corresponds to the recently found (and perhaps less known) phenomenon, sine-square deformation. The latter yields the well-known entanglement entropy. I will present a comprehensive treatment of these three quantizations and discuss its physical implications.