论文标题
有关Wilson Toroidal网络和圆环块的更多信息
More on Wilson toroidal networks and torus blocks
论文作者
论文摘要
我们考虑Chern-Simons的Wilson Line网络$ 3D $重力理论具有圆环边界条件，该理论计算了整个脱离质量运算符的全球保形块$ 2D $ CFT。在总结并进一步扩展了文献中已知结果的一般讨论之后，我们明确地通过$ sl的不可降低有限维表示，通过toroidal wilson网络运算符的特定矩阵元素获得了单点圆环和两点圆环块（2，\ mathbb {r}）$ algebra。结果表达式以两种替代形式给出，以不同的方式处理$ sl（2，\ mathbb {r}）$表示的多种张量产品：（1）$ 3MJ $ WIGNER符号和较高价的互穿，（2）完全对称的张量产品，完全对称的张量产品的基本张量$ sl（2，\ mathbbbbbbbbbb {r r}）$。
We consider the Wilson line networks of the Chern-Simons $3d$ gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus $2d$ CFT. After general discussion that summarizes and further extends results known in the literature we explicitly obtain the one-point torus block and two-point torus blocks through particular matrix elements of toroidal Wilson network operators in irreducible finite-dimensional representations of $sl(2,\mathbb{R})$ algebra. The resulting expressions are given in two alternative forms using different ways to treat multiple tensor products of $sl(2,\mathbb{R})$ representations: (1) $3mj$ Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor products of the fundamental $sl(2,\mathbb{R})$ representation.
