论文标题
边界条件和共形场理论的异常在1+1维
Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
论文作者
论文摘要
我们研究了1+1个维度中形式不变边界条件与共形场理论（CFTS）异常之间的关系。对于具有全局对称性的给定CFT，我们考虑与CFT相关的对称间隙势。如果仅在系统的一个子区域中引入间隙电势，则它为CFT提供了一定的边界条件。从这种等价性中，如果存在一个基本的边界状态，该状态在对称性下是不变的，则可以通过添加相应的间隙势来将CFT与唯一的接地状态相处。这意味着CFT的对称性是无异常的。使用这种方法，我们系统地推断出具有多种对称性的各种CFT的无异常条件。它们包括免费的紧凑型玻色子理论，Wess-Zumino-witten模型和统一的最小模型。当CFT的对称性异常时，它意味着系统的Lieb-Schultz-Mattis型配置性。我们的结果与文献中已知的结果一致。此外，我们将讨论扩展到其他对称性，包括自旋组和广义时间反转对称性。
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.
