论文标题
CFT的全息变量$ _2 $与重型操作员的共形块
Holographic variables for CFT$_2$ conformal blocks with heavy operators
论文作者
论文摘要
我们认为，带有$ n-k $背景重型运营商和$ k $扰动重型运营商的$ c $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n。重型运营商的整形尺寸与大$ C $线性缩放，而分为背景/扰动操作员则假设了额外的扰动扩展。可以在单型方法中计算这种保形块，该方法基本上还原以求解辅助二阶二阶方程并找到溶液的单构型。我们表明，存在我们称为全息图的特定变量，其使用极大地简化了整个分析。因此，我们制定了大型$ c $块的统一特性，该块指出，在全息变量中，它们的形式仅取决于扰动重型操作员的数量。另一方面，全息变量在整体空间中编码度量标准，以便具有相同数量的扰动算子的保形块由相同的地理树计算出来，但在背景操作员创建的不同几何形状上计算出来。
We consider large-$c$ $n$-point Virasoro blocks with $n-k$ background heavy operators and $k$ perturbative heavy operators. Conformal dimensions of heavy operators scale linearly with large $c$, while splitting into background/perturbative operators assumes an additional perturbative expansion. Such conformal blocks can be calculated within the monodromy method that basically reduces to solving auxiliary Fuchsian second-order equation and finding monodromy of solutions. We show that there exist particular variables that we call holographic, use of which drastically simplifies the whole analysis. In consequence, we formulate the uniformization property of the large-$c$ blocks which states that in the holographic variables their form depends only on the number of perturbative heavy operators. On the other hand, the holographic variables encode the metric in the bulk space so that the conformal blocks with the same number of perturbative operators are calculated by the same geodesic trees but on different geometries created by the background operators.
