从模型波函数计算中心荷和准空穴标度维数：Jack波函数与W-代数的关系
Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
摘要：
本文提出了一种直接从基态和准空穴波函数得到中心荷和准空穴标度维数的一般方法。我们的方法适用于满足特定的聚类特性的波函数。然后，我们使用我们的方法来检查杰克对称函数和某些W-代数之间的关系。通过计算两种情况下某些场的中心荷和标度维数，证明了（k，r）容许Jack函数与共形场论W_k（k+1，k+r）的标度因子是一致的。对于由酉W模型描述的Jacks，中心荷和准空穴指数与先前通过分析边缘激发的物理学获得的指数相匹配。对于非么正W模型描述的Jacks，由波函数得到的中心荷和准空穴标度维数与由边缘物理得到的不同，而与相应W模型的“有效”中心荷一致.
英文摘要：
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.
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