成簇性质、Jack多项式和酉共形场论
Clustering properties, Jack polynomials and unitary conformal field theories
摘要：
最近，Jack多项式被提出作为描述非阿贝尔分数量子Hall系统的Z_k Read-Rezayi态的自然推广。证明了这些多项式与基于李代数A_{k-1}的一类W-共形场论的关联函数有关。这些理论可以看作是具有Z_k对称性的更一般的CFTs系列的非幺正解，即仿费米子理论。从观察到，一些parafermionic理论承认酉解，以及，我们表明，通过计算相应的关联函数，这些理论提供的试验波函数满足相同的聚类特性的非酉的。我们明确地表明，虽然由酉CFTs构造的波函数不能表示为一个单一的杰克多项式，他们仍然表现出一个精细的结构，杰克多项式的数学性质发挥了重要作用。
英文摘要：
Recently, Jack polynomials have been proposed as natural generalizations of Z_k Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A_{k-1}. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z_k symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.
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