（1+1）d有理共形场论中的相对反常
Relative Anomaly in (1+1)d Rational Conformal Field Theory
摘要：
本文研究了（1+1）d空间中的富维有理共形场论（RCFT）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（1+1）d非手性RCFTs和（2+1）d双重拓扑（SET）相位之间的精确对应关系，并选择对称的间隙边界。基于这些结果，我们推导出一个一般公式的相对特胡夫特异常的代数数据，表征SET阶段和它的边界。
英文摘要：
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 non-chiral RCFTs and (2+1)d doubled 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.
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