论文标题
异常对称在边界末端
Anomalous Symmetries End at the Boundary
论文作者
论文摘要
如果不能将量子场理论的全球对称性升级为“ hooft异常”，那么如果不能将其提升为量规理论的局部对称性。在本文中，我们表明异常也是定义对称边界条件的障碍。这也适用于Lorentz与重力异常的对称性。对于具有扰动异常的理论，我们通过分析边界存在下的Wess-Zumino一致性条件和当前病房身份来证明障碍。然后，我们从对称缺陷方面重新解决了问题，并找到了与离散和方向逆转的全局对称性异常相同的结论，直到猜想是全局引力异常可能与任何差异形态对称性无关，也可能与边界条件存在相关。该猜想适用于已知的引力异常中的$ d \ le 3 $，这使我们能够以$ d \ le 4 $的形式得出结论。
A global symmetry of a quantum field theory is said to have an 't Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in the presence of a boundary. We then recast the problem in terms of symmetry defects and find the same conclusions for anomalies of discrete and orientation-reversing global symmetries, up to the conjecture that global gravitational anomalies, which may not be associated with any diffeomorphism symmetry, also forbid the existence of boundary conditions. This conjecture holds for known gravitational anomalies in $D \le 3$ which allows us to conclude the obstruction result for $D \le 4$.
