Bernevig, B. Andrei and Gurarie, Victor and Simon, Steven H.
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).
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.
||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
||Central Charge; Quasihole; Scaling; Dimensions; Model Wavefunctions;
Jack Wavefunctions; W-algebras;
||Science & Engineering > Mathematical Physics
Steven H. Simon
||02 Sep 2011 14:47
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||Journal of Physics A: Mathematical and Theoretical
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