论文标题
弯曲的域壁费米及其异常流入
Curved domain-wall fermion and its anomaly inflow
论文作者
论文摘要
我们研究了$ u（1）$量规场对具有弯曲域壁质量术语的晶格费米昂系统的效果。手性边缘模式与传统的平面壁壁费米恩一样，出现在墙壁上，其狄拉克操作员包含诱导的重力电势以及$ u（1）$ vector的电势。在二维平坦晶格上的$ s^1 $域壁费米，我们在迪拉克特征值频谱中发现了aharonov-bohm（AB）效应与重力间隙之间的竞争，这导致了时间倒流的异常（$ t $）对称性。我们的数值结果与$ s^1 $域壁的磁盘上的atiyah-patodi-singer索引定理表现出良好的一致性，该磁盘描述了大体和边缘之间$ t $异常的取消。当$ u（1）$通量被挤入一个plaquette中时，AB阶段采用量化的值$π$ mod $2π\ mathbb {z} $时，异常流入的流入发生了巨大变化：强烈的磁通材料周围的另一个域壁围绕着磁通量，使两个零模式与两个零模式相交。在存在磁性单极的情况下，在$ S^2 $域壁费米子中也观察到了这种现象。我们发现，围绕单极壁的域壁创建在微观上解释了witten效果。
We investigate the effect of $U (1)$ gauge field on lattice fermion systems with a curved domain-wall mass term. In the same way as the conventional flat domain-wall fermion, the chiral edge modes appear localized at the wall, whose Dirac operator contains the induced gravitational potential as well as the $U(1)$ vector potential. In the case of $S^1$ domain-wall fermion on a two-dimensional flat lattice, we find a competition between the Aharonov-Bohm(AB) effect and gravitational gap in the Dirac eigenvalue spectrum, which leads to anomaly of the time-reversal ($T$) symmetry. Our numerical result shows a good consistency with the Atiyah-Patodi-Singer index theorem on a disk inside the $S^1$ domain-wall, which describes the cancellation of the $T$ anomaly between the bulk and edge. When the $U(1)$ flux is squeezed inside one plaquette, and the AB phase takes a quantized value $π$ mod $2π\mathbb{Z}$, the anomaly inflow drastically changes: the strong flux creates another domain-wall around the flux to make the two zero modes coexist. This phenomenon is also observed in the $S^2$ domain-wall fermion in the presence of a magnetic monopole. We find that the domain-wall creation around the monopole microscopically explains the Witten effect.
