论文标题
CFT Unitarity和Ads Cutkosky规则
CFT Unitarity and the AdS Cutkosky Rules
论文作者
论文摘要
我们以弱耦合和强耦合得出了保形场理论（CFTS）的Cutkosky规则。这些规则给出了一种简单的图形方法，以计算出现在洛伦兹倒置公式中的双重交换器。我们首先在平面空间中重新访问弱耦合的CFT，在Feynman图上进行切割。然后，我们将这些规则推广到强耦合全息CFT，其中切割是在双重理论的Witten图上进行的。在这两种情况下，Cutkosky规则将循环图将循环图分配到壳上的子三图中，并推广标准的S-矩阵切割规则。这些规则是自然制定的，并在洛伦兹动量空间中得出，在洛伦兹动量空间中，双重交换器显然与CFT光学定理相关。最后，我们在树级和一个循环的明确示例中研究了广告剪切规则。在这些示例中，我们确认规则与OPE限制一致，并且我们在平面限制中恢复了S-Matrix光学定理。这些广告削减规则和CFT分散公式共同形成了一种全息单位方法，以从其切割中重建Witten图。
We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.
