论文标题
在保形固定点上的异常病房身份
Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
论文作者
论文摘要
共形对称是许多无质量量子场理论的基础，但是对于这种强大的对称性对壳散射幅度的后果知之甚少。在保形固定点上，在尺寸规范的$ ϕ^3 $模型中工作，我们表明，壳上骨的振幅满足异常的保形病房身份。每个外部壳状状态对异常贡献两个术语。第一项与基本场异常维度成正比，因此仅涉及较低环的信息。我们表明，第二项可以作为通用共线函数和低阶振幅的卷积。因此，保形异常的计算比在相同的扰动顺序上的幅度要简单，这使我们的异常保形病房身份在扰动理论中具有强大的预测能力。最后，我们表明我们的结果对于距离固定点的尺寸规范化的振幅也具有实际重要性。
Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell scattering amplitudes. Working in a dimensionally-regularised $ϕ^3$ model at the conformal fixed point, we show that the on-shell renormalised amplitudes satisfy anomalous conformal Ward identities. Each external on-shell state contributes two terms to the anomaly. The first term is proportional to the elementary field anomalous dimension, and thus involves only lower-loop information. We show that the second term can be given as the convolution of a universal collinear function and lower-order amplitudes. The computation of the conformal anomaly is therefore simpler than that of the amplitude at the same perturbative order, which gives our anomalous conformal Ward identities a strong predictive power in perturbation theory. Finally, we show that our result is also of practical importance for dimensionally-regularised amplitudes away from the conformal fixed point.
