论文标题
关于自由理论的异常电流的注意
Note on anomalous currents for a free theory
论文作者
论文摘要
最近发现，由于Weyl异常，外部磁场可以在边界附近诱导异常电流。在本说明中，我们研究了一般维度的复杂标量和狄拉克场的异常电流。我们开发了一种扰动方法，以通过边界计算绿色的函数。通过应用此方法，我们获得了一个半空间和条带的磁场线性阶序的异常电流。据我们所知，Dirac Fermions和Strips的结果是新的。值得注意的是，与标量和全息bcft不同，狄拉克场的异常电流独立于一般维度的边界条件。此外，狄拉克场的电流总是比复杂标量的电流大。最后，我们在半空间中发现了异常电流的正式表达。结果以动量积分表示，可以通过数值评估。我们发现质量会按预期抑制异常电流。
Recently it is found that, due to Weyl anomaly, an external magnetic field can induce anomalous currents near a boundary. In this note, we study anomalous currents for complex scalars and Dirac fields in general dimensions. We develop a perturbation method to calculate Green's function in the spacetime with boundaries. By applying this method, we obtain anomalous currents up to the linear order of magnetic fields in a half space and in a strip. To the best of our knowledge, the results for Dirac fermions and for strips are new. It is remarkable that, unlike the scalars and holographic BCFT, the anomalous currents of Dirac fields are independent of boundary conditions in general dimensions. Besides, the currents of Dirac fields are always larger than those of complex scalars. Finally, we find an exact formal expression of the anomalous current in a half space. The result is expressed in momentum integrals, which can be evaluated numerically. We find that the mass suppresses the anomalous currents as expected.
