SCFT中c=3/2的AGT基和Uglov多项式
AGT basis in SCFT for c=3/2 and Uglov Polynomials
摘要：
AGT允许一个计算共形块的d = 2 CFT的一大类手征CFT代数。这与（广义）手征代数模中存在某种正交基有关。基的元素是某个可积模型的特征向量，一般用N元组的杨氏图来标记。特别是，人们发现，在Virasoro的情况下，这些向量表示的杰克多项式，标记为2元组的普通杨图，并为超级Virasoro的情况下，他们有关的Uglov多项式，标记为两个彩色杨图。在一般中心荷的情况下，当其中一个杨氏图为空时，检查该陈述。本文研究了N=1的SCFT，并利用该基构造了4点关联函数。为此，我们需要澄清基元和Uglov多项式之间的联系，我们还需要使用两个玻色化及其与反射算子的联系。对于中心荷$c=3/2$，我们检查了整个图集与Uglov多项式的联系。
英文摘要：
AGT allows one to compute conformal blocks of d = 2 CFT for a large class of chiral CFT algebras. This is related to the existence of a certain orthogonal basis in the module of the (extended) chiral algebra. The elements of the basis are eigenvectors of a certain integrable model, labeled in general by N-tuples of Young diagrams. In particular, it was found that in the Virasoro case these vectors are expressed in terms of Jack polynomials, labeled by 2-tuples of ordinary Young diagrams, and for the super-Virasoro case they are related to Uglov polynomials, labeled by two colored Young diagrams. In the case of a generic central charge this statement was checked in the case when one of the Young diagrams is empty. In this note we study the N=1 SCFT and construct 4 point correlation function using the basis. To this end we need to clarify the connection between basis elements and Uglov polynomials, we also need to use two bosonizations and their connection to the reflection operator. For the central charge $c=3/2$ we checked that there is a connection with the Uglov polynomials for the whole set of diagrams.
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