论文标题
$ \ hat {\ mathfrak {sl_2}} $的2D CFT和NULL向量的圆环单点块
The torus one-point block of 2d CFT and null vectors in $\hat{\mathfrak{sl_2}}$
论文作者
论文摘要
该论文分为两个部分，在第一部分中，我们研究了Zamolodchikov递归关系框架中Virasoro 1分块的计算。人们普遍认为，这种递归关系包含中央电荷$ c $中的非物理杆。在每个顺序上，我们猜想了杆的自由表达式如何取决于内部和外部的共形尺寸和中央电荷，并提出了如何以数值计算它。在本论文中，我们将POL的自由表达式计算为4。在第二部分中，我们引入了具有额外对称性的保形场理论，由仿射lie代数$ \ hat的最高权重表示{\ mathfrak {\ mathfrak {sl}}} _ 2 $描述。在1级，我们确定了一个通用$ \ mathfrak {sl} _2 $ basit-distentent的'null Operator'，该'null Operator'在通常的意义上生成了null向量。 “零操作员”是通用的对象，可以应用于水平表示的任何状态，产生零向量，因此与水平表示的选择无关。
This thesis is divided into two parts, where in the first part we investigate the computation of Virasoro 1-point blocks on the torus in the framework of Zamolodchikov's recursion relation. It is widely accepted that this recursion relation contains unphysical poles in the central charge $c$. At each order we conjecture how the pole free expressions depend on the internal and external conformal dimensions and central charge, and propose how to compute it numerically. In this thesis, we have calculated the pole free expression up to order 4. In the second part we introduce a conformal field theory with an extra symmetry, described by highest weight representations of the affine Lie algebra $\hat{\mathfrak{sl}}_2$. At level 1, we determined a universal $\mathfrak{sl}_2$ basis-independent 'null operator', which generates null vectors in the usual sense. The 'null operators' are generalized objects and can be applied to any state of the horizontal representation, yielding null vectors and are therefore independent from the choice of horizontal representations.
