反常与玻色化
Anomalies and Bosonization
摘要：
最近，已经开发了超过1+1维的玻色化的一般方法。在这篇文章中，我们回顾这些玻色化，并将其扩展到边界条件的情况。特别地，我们研究了当体理论是一个$G$ -对称性保护的拓扑相，而边界理论有一个$G$ 't Hooft反常时的情形.我们讨论了如何，当异常是不可实现的玻色子系统中，$G$对称代数成为修改玻色子化的异常理论。这给了我们一个有用的工具来理解费米子系统的异常，因为没有办法计算异常多项式的边界规范变化，因为玻色子系统的异常。我们以1+1D的手征异常和2+1D的宇称/时间反转异常为例进行了研究。我们还提供了一个衍生的SPT阶段与域缺陷装饰$p+ip$超导体和Kitaev字符串的新的约束。
英文摘要：
Recently, general methods of bosonization beyond 1+1 dimensions have been developed. In this article, we review these bosonizations and extend them to the case with boundary conditions. In particular, we study the case when the bulk theory is a $G$-symmetry protected topological phase and the boundary theory has a $G$ 't Hooft anomaly. We discuss how, when the anomaly is not realizable in a bosonic system, the $G$ symmetry algebra becomes modified in the bosonization of the anomalous theory. This gives us a useful tool for understanding anomalies of fermionic systems, since there is no way to compute a boundary gauge variation of the anomaly polynomial, as one does for anomalies of bosonic systems. We take the chiral anomalies in 1+1D and the parity/time reversal anomalies in 2+1D as case studies. We also provide a derivation of new constraints in SPT phases with domain defects decorated by $p+ip$ superconductors and Kitaev strings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
