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

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

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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 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.

Item Type: Article
Additional Information: B.A.B thanks F.D.M. Haldane for countless discussions and suggestions. B.A.B. also wishes to thank P. Bonderson, N. Regnault, L. Tevlin, R. Thomale and E. Ardonne for discussions. V.G. acknowledges support from NSF grant, DMR-0449521. V.G. also acknowledges helpful discussions with C. Nayak. S.H.S acknowledges helpful discussions with P. Fendley, E. Ardonne, J. Slingerland, and particularly E. Rezayi and N. Read
Keywords: Central Charge; Quasihole; Scaling; Dimensions; Model Wavefunctions; Jack Wavefunctions; W-algebras;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2693
Identification Number: 10.1088/1751-8113/42/24/245206
Depositing User: Steven H. Simon
Date Deposited: 02 Sep 2011 14:47
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: Institute of Physics Publishing Ltd
Refereed: No
URI:

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