论文标题
精确的量子共形对称性，自发分解和重力Weyl异常
Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
论文作者
论文摘要
如果将希格斯玻色子的质量放到零，则标准模型的经典拉格朗日享受了整形群的对称性。这是一个暗示，在描述性质的最终理论中，形成对称性可能起着基本作用。尺度的起源（例如希格斯真空期望值（VEV））可能是由于dilaton场对共形对称性的自发分解而产生的。在这项工作中，我们研究是否可以通过量子理论实施这种经典的设置，并通过呈现明确的结构，在现象学上可行，在该结构中可以保留确切的保形对称性，并且在自发损坏的同时是无异常的。不仅是希格斯的质量，而且是QCD限制半径等真正的量子尺度。我们还以动态性的重力讨论了这些思想向理论的扩展，并表明无异常的局部Weyl变换的唯一有限亚组与全球尺度对称对应。这意味着平面理论的共形不变性被与Weyl异常有关的重力效应明确分解为尺度对称性。
The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.
