Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras

TL;DR

This paper introduces a method to extract central charge and quasihole scaling dimensions directly from wavefunctions, linking Jack functions to W-algebras and comparing theoretical predictions with physical edge excitations.

Contribution

It provides a novel approach to connect wavefunction properties with conformal field theory data, specifically relating Jack wavefunctions to W-algebras and their central charges.

Findings

Matching central charges for unitary W-models and wavefunctions.

Discrepancies in non-unitary cases between wavefunction and edge physics.

Evidence supporting the correspondence between Jack functions and W-algebra correlators.

Abstract

We present a general method to obtain the central charge and quasihole scaling dimension directly from groundstate 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 W_k(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 the ones 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 the ones obtained from the edge physics, which instead agree with the "effective" central charge of the corresponding W-model.