论文标题
用于旋转WITTEN图表的双形式形式主义
A Bispinor Formalism for Spinning Witten Diagrams
论文作者
论文摘要
我们为广告$ _4 $和CFT $ _3 $开发了一种新的嵌入空间形式主义，这对于评估旋转操作员的Witten图很有用。基本变量是杀死散装广告$ _4 $的旋转器，以及边界CFT $ _3 $的共形杀死旋转器。在这些新变量中，较常规的嵌入空间坐标$ x^i $，边界的$ p^i $是双线性。我们为一般的散装式传播器编写了一个简单的紧凑形式，对于Spin $ \ ell \ geq 1 $的边界运算符，我们确定其在单位性结合处的保护属性。在我们的cft $ _3 $形式主义中，我们确定了一个差异操作员的$ \ mathfrak {so}（so}（5,5）$ lie代数，其中包括基本的重量转移操作员。这些操作员以及ADS $ _4 $中的一组差分运算符可用于将Witten图与旋转的外腿与仅具有标量外腿的Witten图相关联。我们提供了几种应用程序，其中包括康普顿散射以及对广告$ _4 $中的$ r^4 $联系交互的评估。最后，我们为大型旋转器和矢量规场的散装传播剂提供了双平方公式，并评估了用旋转器交换的图表。
We develop a new embedding-space formalism for AdS$_4$ and CFT$_3$ that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS$_4$ and conformal Killing spinors for the boundary CFT$_3$. The more conventional embedding space coordinates $X^I$ for the bulk and $P^I$ for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin $\ell \geq 1$, we determine its conservation properties at the unitarity bound. In our CFT$_3$ formalism, we identify an $\mathfrak{so}(5,5)$ Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS$_4$, can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an $R^4$ contact interaction in AdS$_4$. Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.
