论文标题
项链频道中的圆环形成块和卡西米尔方程
Torus conformal blocks and Casimir equations in the necklace channel
论文作者
论文摘要
我们考虑在圆环上二维保形场理论的任意交换通道中的共形块分解。通道是由用外腿（项链子三图）构建的图表来描述的，三价顶点形成了附着在项链上的三价树。然后，可以通过与$ k $ -point torus block上的许多OPE操作员在项链通道中的$ k = 1，...，n $上的$ n $ - 点圆环结构块可获得。我们专注于项链频道，转到大$ C $制度，那里的Virasoro代数将截断为$ SL（2，\ Mathbb {r}）$ subalgebra，并获得相应$ k $ k $ point的全局全球构造块的Casimir方程系统。在平面限制中，当圆环模块化参数$ q \ to 0 $时，我们明确地在平面上找到了Casimir方程，该平面定义了$（k+2）$ - 梳子通道中的point Goint Global Sonformal Block。最后，我们制定了一般方案，以在任意通道中找到全球圆环块的Casimir方程。
We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram) and trivalent vertices forming trivalent trees attached to the necklace. Then, the $n$-point torus conformal block in any channel can be obtained by acting with a number of OPE operators on the $k$-point torus block in the necklace channel at $k=1,...,n$. Focusing on the necklace channel, we go to the large-$c$ regime, where the Virasoro algebra truncates to the $sl(2, \mathbb{R})$ subalgebra, and obtain the system of the Casimir equations for the respective $k$-point global conformal block. In the plane limit, when the torus modular parameter $q\to 0$, we explicitly find the Casimir equations on a plane which define the $(k+2)$-point global conformal block in the comb channel. Finally, we formulate the general scheme to find Casimir equations for global torus blocks in arbitrary channels.
