论文标题
全局异常在较高维度$ \ mathbb {cp}^{n-1} $模型中匹配
Global anomaly matching in higher-dimensional $\mathbb{CP}^{N-1}$ model
论文作者
论文摘要
我们调查了$ \ mathbb {cp}^{n-1} $模型中的hooft异常，该模型高于两种，并识别两种异常：一种是$ \ mathrm {psu}（n）$调味和磁性符号和磁性和磁性的混合异常。后者表明，即使在没有风味对称性的情况下，只要尊重反射和磁对称性，模型就无法具有独特的间隙基态。我们还阐明了在单极变形下生存的't Hooft异常的条件，该变形明确将磁对称分解为离散亚组。此外，我们明确地展示了在低能量的对称性破碎相的有效描述中识别的“ hoft异常”如何匹配---néel，$ \ mathrm {u}（1）$ spin Liquid和Valence Bond Liquid和Valence Bond固体相位。还讨论了四维$ \ mathbb {cp}^{n-1} $模型的有限温度相图的应用。
We investigate 't Hooft anomalies in the $\mathbb{CP}^{N-1}$ model in spacetime dimensions higher than two and identify two types of anomalies: One is a mixed anomaly between the $\mathrm{PSU}(N)$ flavor-rotation and magnetic symmetries, and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases---the Néel, $\mathrm{U}(1)$ spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional $\mathbb{CP}^{N-1}$ model is also discussed.
