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arXiv 1904.04833hep-thcond-mat.str-el
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荷算子的反常与界

Anomalies and Bounds on Charged Operators

Ying-Hsuan Lin, Shu-Heng Shao

备注：
49+16 pages, 19 figures, 1 table; v2: minor clarifications; v3: typos fixed
发表信息：
Phys. Rev. D 100, 025013 (2019)
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摘要：

本文研究了T Hooft反常（即规范的障碍）对共形场论的影响，重点讨论了当整体对称性为$\mathbb{Z_2}$时的情形。利用模自举法，导出了具有$\mathbb{Z_2}$整体对称性的（1+1）维玻色共形场论的普适界。自举边界极大地依赖于特胡夫特异常。特别地，当对称性为反常时，最轻的$\mathbb{Z_2}$奇算子存在一个普适上界，而当对称性为非反常时，则没有上界。在非反常情况下，我们发现最轻的$\mathbb{Z_2}$奇态和缺陷基态不可能都是任意重的。我们还考虑具有$U(1)$全局对称性的理论，并评论说，如果对称性是非异常的，则最轻的$U(1)$带电算符没有界限。

英文摘要：

We study the implications of 't Hooft anomaly (i.e. obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is $\mathbb{Z_2}$. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal $\mathbb{Z_2}$ global symmetry are derived. The bootstrap bounds depend dramatically on the 't Hooft anomaly. In particular, there is a universal upper bound on the lightest $\mathbb{Z_2}$ odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. In the non-anomalous case, we find that the lightest $\mathbb{Z_2}$ odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a $U(1)$ global symmetry, and comment that there is no bound on the lightest $U(1)$ charged operator if the symmetry is non-anomalous.

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