Reconstruction of the conformal algebra from a critical groundstate on the (fuzzy) sphere

Recently, we found a method to reconstruct the dilatation operator (sphere Hamiltonian) from a regulated conformal field theory groundstate. In this paper, we explore methods to construct the whole global conformal algebra, and test our construction using fuzzy sphere regularization. Starting from a groundstate of the same Hamiltonian, these methods perform better than constructions of the conformal generators based on a Hamiltonian density, are model-independent, require no additional tuning, and improve with system size. One purpose of reconstructing the conformal algebra is to identify conformal primary states, which we do with some success. We also find further evidence supporting the model of the short-distance corrections to the entanglement Hamiltonian proposed earlier and use it to make systematic improvements.