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Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
Bernevig, B. Andrei; Gurarie, Victor; Simon, Steven H.
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 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 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.
Keyword(s): Mathematical Physics; Central Charge; Quasihole; Scaling; Dimensions; Model Wavefunctions; Jack Wavefunctions; W-algebras
Publication Date:
2009
Type: Journal article
Peer-Reviewed: No
Institution: Maynooth University
Citation(s): Bernevig, B. Andrei and Gurarie, Victor and Simon, Steven H. (2009) Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras. Journal of Physics A: Mathematical and Theoretical, 42 (245206). pp. 1-30. ISSN 1751-8113
Publisher(s): Institute of Physics Publishing Ltd
File Format(s): application/pdf
Related Link(s): http://eprints.maynoothuniversity.ie/2693/1/AB_Central_Charge.pdf
First Indexed: 2014-09-20 05:04:50 Last Updated: 2014-09-20 05:04:50