标题： 一维和二维共形场论的边界条件和反常 显示英文标题

标题： Boundary conditions and anomalies of conformal field theories in 1+1 dimensions

摘要： 我们研究了在一维共形场论(CFTs)中保形不变边界条件与反常之间的关系。对于具有全局对称性的给定CFT，我们考虑对CFT是相关扰动的对称间隙势。如果间隙势仅在一个系统子区域中引入，则它为CFT提供了一定的边界条件。通过这种等价性，如果存在一个在对称性下不变的Cardy边界态，则可以通过添加相应的间隙势使CFT具有唯一的基态，从而实现间隙化。这意味着CFT的对称性没有反常。使用这种方法，我们系统地推导了各种具有不同对称性的CFT的无反常条件。这些包括自由紧致玻色子理论、Wess-Zumino-Witten模型和幺正最小模型。当CFT的对称性出现反常时，意味着系统的Lieb-Schultz-Mattis型无法间隙化。我们的结果与文献中已知的结果一致（在适用的情况下）。此外，我们将讨论扩展到其他对称性，包括自旋群和广义时间反转对称性。 显示英文摘要

摘要： We study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. They include the free compact boson theory, Wess-Zumino-Witten models, and unitary minimal models. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries.