论文标题
分散总和规则的应用：$ε$ - expansion和全息图
Applications of dispersive sum rules: $ε$-expansion and holography
论文作者
论文摘要
我们使用Mellin空间分散关系以及Polyakov条件来得出保形场理论（CFTS）的总和规则。这些总和的定义属性是抑制双重扭转算子的贡献。首先，我们将这些和规则应用于$ d = 4-ε$尺寸的Wilson-Fisher模型。我们将许多已知结果重新列出，以订购$ε^4 $，我们做出了新的预测。没有假设分析性降至旋转$ 0 $。其次，我们研究全息CFT。我们使用分散总和来获得树级和单循环异常维度。最后，我们简要讨论了重型运营商对UV完整全息理论的总和规则的贡献。
We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in $d=4-ε$ dimensions. We re-derive many of the known results to order $ε^4$ and we make new predictions. No assumption of analyticity down to spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.
