Central charge and quasihole scaling dimensions from model wavefunctions: toward relating Jack wavefunctions to W-algebras

We present a general method for obtaining the central charge and the quasihole scaling dimension directly from ground-state and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific clustering properties. We then use our method to examine the relation between Jack symmetric functions and certain W-algebras. We add substantially to the evidence that the (k, r) admissible Jack functions correspond to correlators of the conformal field theory Wk(k+1,k+r) by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. For the Jacks described by unitary W-models, the central charge and quasihole exponents match those previously obtained from analyzing the physics of the edge excitations. For the Jacks described by non-unitary W-models the central charge and quasihole scaling dimensions obtained from the wavefunctions differ from those obtained from the edge physics, which instead agree with the 'effective' central charge of the corresponding W-model