Anomaly and superconnection
Anomaly and superconnection
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异常与超连接
DOI：
10.1093/ptep/ptab131
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发表时间：
2021
影响因子：
3.5
通讯作者：
Sugimoto Shigeki
中科院分区：
文献类型：
--
作者：
Kanno Hayato;Sugimoto Shigeki
我们研究了质量依赖于时空的费米子的反常现象。利用Fujikawa的方法，我们发现与U（N）+×U（N）−手征对称性和U（N）味对称性相关的偶维和奇维反常分别可以用超连接表示。特别地，在偶维和奇维情况下，类向量U（1）对称的反常都是由超连接的Chern特征给出的。本文还指出，D维时空系统的非阿贝尔反常是由超连接的陈特征标的（D+ 2）-形式部分所表征的，它推广了无质量情况下的反常多项式。这些结果使我们能够以统一的方式分析具有界面和时空边界的系统中的异常。应用指标定理，包括Atiyah-Patodi-Singer指标定理和Callias型指标定理，也进行了讨论。此外，我们给出了一个自然的弦理论解释这些结果。
We study anomalies of fermions with spacetime-dependent mass. Using Fujikawa’s method, it is found that the anomalies associated with theU(N)+×U(N)−chiral symmetry andU(N) flavor symmetry for even and odd dimensions, respectively, can be written in terms of superconnections. In particular, the anomaly for a vector-likeU(1) symmetry is given by the Chern character of the superconnection in both even- and odd-dimensional cases. It is also argued that the non-Abelian anomaly for a system inD-dimensional spacetime is characterized by a (D+ 2)-form part of the Chern character of the superconnection which generalizes the usual anomaly polynomial for the massless case. These results enable us to analyze anomalies in the systems with interfaces and spacetime boundaries in a unified way. Applications to index theorems, including the Atiyah–Patodi–Singer index theorem and a Callias-type index theorem, are also discussed. In addition, we give a natural string theory interpretation of these results.