论文标题
关于（1+1）$ d $的异国情调一致的异常：一个鬼故事
On Exotic Consistent Anomalies in (1+1)$d$: A Ghost Story
论文作者
论文摘要
我们在（1+1）$ d $ non-spin量子场理论中回顾了hooft异常，从一致性和局部条件开始，发现一致的u（1）和引力异常不能总是通过正确量化（2+1）$ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $。一方面，我们证明只有通过非反射阳性或非压缩理论才能实现某些外来异常异常。另一方面，在不坚持反射阳性的情况下，外来异常对流入范式提出了警告。对于混合的U（1）引力异常，我们提出了一种涉及混合u（1）$ \ times $ so（2）经典的Chern-Simons动作的流入机制，其边界条件与SO（2）量规场与（1+1）$ D $ spin连接匹配。此外，我们表明这种混合异常会导致U（1）拓扑缺陷线的同位素异常。同位素异常可以通过外部曲率改进项来取消，但以创建周期性异常为代价。我们调查了Holomorthic $ bc $ Ghost System，该系统意识到所有异国情调的一致异常，并以对U（1）有限亚组异常的微妙评论结尾。
We revisit 't Hooft anomalies in (1+1)$d$ non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)$d$ classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1)$\times$SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)$d$ spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic $bc$ ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).
