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AGT basis in SCFT for c = 3/2 and Uglov polynomials
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-07-30 , DOI: 10.1016/j.nuclphysb.2020.115133
Vladimir Belavin , Abay Zhakenov

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.



中文翻译:

SCFT中c = 3/2和Uglov多项式的AGT基础

AGT可以为一大类手性CFT代数计算d = 2 CFT的保形块。这与(扩展的)手性代数的模中存在一定的正交基有关。基础的元素是某个可积模型的特征向量,通常由Young图的N元组标记。尤其是,发现在维拉索罗的情况下,这些向量用Jack多项式表示,用普通的Young图的2元组标记;对于超维拉索罗的情况,它们与Uglov多项式有关,用两个有色的Young标记。图。如果是通用中央收费,则在其中一个杨图为空的情况下,将检查此语句。在本文中,我们研究了N = 1 SCFT并使用该基础构造了4点相关函数。为此,我们需要阐明基本元素和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符的联系。对于中央收费C=3/2 我们检查了整个图集与Uglov多项式之间的关系。

更新日期:2020-08-10
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