Relative anomaly in ( 1+1 )d rational conformal field theory
Relative anomaly in ( 1+1 )d rational conformal field theory
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DOI：
10.1103/physrevresearch.2.043044
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
M. Cheng;D. Williamson
中科院分区：
文献类型：
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作者：
M. Cheng;D. Williamson
本文研究了（1+1）d空间中的富维有理共形场论的t Hooft反常。这种反常现象决定了一个理论是否可以在一个真正的（1+1）维系统中实现，或者在（2+1）维拓扑相的边缘上实现。在其手征代数上具有相同对称作用的RCFTs，由于局部准素算子上的附加对称荷，可能具有不同的t Hooft反常。为了计算相对异常，我们建立了一个精确的对应关系（1+1）d RCFTs和（2+1）d的富拓扑（SET）相位与选择的对称间隙边界。基于这些结果，我们根据表征SET相及其边界的代数数据推导出相对特胡夫特异常的一般公式。
We study 't Hooft anomalies of symmetry-enriched rational conformal field theories (RCFT) in (1+1)d. Such anomalies determine whether a theory can be realized in a truly (1+1)d system with on-site symmetry, or on the edge of a (2+1)d symmetry-protected topological phase. RCFTs with the identical symmetry actions on their chiral algebras may have different 't Hooft anomalies due to additional symmetry charges on local primary operators. To compute the relative anomaly, we establish a precise correspondence between (1+1)d RCFTs and (2+1)d symmetry-enriched topological (SET) phases with a choice of symmetric gapped boundary. Based on these results we derive a general formula for the relative 't Hooft anomaly in terms of algebraic data that characterizes the SET phase and its boundary.